You are correct that there are infinitely many possibilities for what deities might exist and how they might punish or reward you for how you live your life. It's a common criticism raised against some religious arguments (especially Pascal's wager, and also the Kalam cosmological argument).
This, however, doesn't mean it's not an important question. If there are possibilities, that suggests that one of those possibilities could be true. It may still be that one or more gods exists, and we may have some empirical evidence, arguments or other ways to determine (to some degree) what a god, if a god exists, is capable of, what they want from us, what traits they have, etc. Similarly, we may determine that a god with certain traits cannot exist.
For instance, one could argue that an all-loving and all-powerful god would be inconsistent with the existence of the large amounts of seemingly-unnecessary suffering we see in the world (related: the problem of evil), or with eternal punishment (especially when combined with the existence of non-resistant non-belief), or with the idea of one being punished for the crimes of another, or with their inspired book containing moral atrocities or inconsistencies.
Don't waste too much time on it
I would say that after you've considered the strongest arguments from both / all / a few sides, and failed to find any good reason to believe a god exists, there probably isn't much sense in continuing the search.
It's possible, if you dedicate every waking moment to trying to find out whether a deity exists, that you may find one. But if you do a cost-benefit analysis, you may find that spending your time on other things would provide far greater benefit. That's my conclusion, anyway.
Having considered the evidence and arguments available, it seems exceedingly unlikely I'd find that a deity exists, and close to impossible that they would exercise some eternal consequences on me for how I live.
As such, dedicating much of what's likely the only life I have, to pursue something I'm unlikely to find, doesn't seem particularly reasonable. There may be eternal consequences, but only if a deity with particular traits exists. Otherwise, it's a question of what fraction of your one life you're dedicating to this question.
What is "looking for god", anyway?
There may also be a bit of a misnomer in "looking for god", since there are also infinitely many ways a deity might present themselves.
Ones that (in a manner of speaking) beam things into your brain or which you can speak to by just thinking is just a particular (if popular) subset of possible deities. If you want to consider all possible deities, you'll have to look in every possible way, in every possible place. In that sense, these claims can all be considered distinct (if perhaps mutually exclusive).
Every moment spent looking for the brain-beaming deities, is a moment not spent looking for the signs-on-toast deities or the pictures-on-leaves deities or the human-sacrifice deities or any others.
Unless you have a way to narrow it down, there are infinitely-many possible deities, and also infinitely-many possible places you can look for them. So the expected benefit from anything you can possibly try in your finite life is essentially zero, even if one such deity exists, and it's possible to find them (which is already way too much to grant for the sake of argument).
One might narrow it down to popular religions, on the premise that this deity might've specifically revealed themselves to some or otherwise made it more likely that they're be found. That's why I started from "after you've considered the strongest arguments".
A god that punishes seeking truth?
A god that punishes one for seeking truth is also a possibility, but you can't really account for that, because not seeking truth would prevent you from establishing whether a god with (almost) any other traits exists.
A deity should be self-evident
As a somewhat trivial argument, one might say that if a deity exists that wants you to act in a particular way or would punish or reward you for how you act, they would make their existence self-evident to you, prior to and independent of you taking any action yourself. Since no deity is self-evident to you, no such deity exists.
Given its simplicity, I suspect people may underestimate the strength of the argument (not that any argument is perfect). Although it may be best used in conjunction with a consideration of evidence and arguments that people present, to just serve to increase your confidence in not accepting the existence of deities. And it seems unlikely to convince anyone else that their deity doesn't exist.
Plenty of theists say the existence of their particular deity is self-evident, but this is either the result of fallaciously equivocating (e.g. God is love and everyone experiences love) or the assertion/conclusion contradicts the available evidence. They could perhaps argue that it's self-evident to them, which I'd still disagree with, but it's clearly not self-evident to everyone else, by any reasonable metric. It's most definitely not self-evident to me, although that only serves to refute their claim for myself and not for others, since I'm the only one with direct access to my mental state.
On a related note, see the question If we can't know whether a divine being exists, would that being be unimportant even if it did exist? and my answer there.
Beliefs inform actions and actions have consequences
Whether a deity exists is also an important question because other people believe it.
This doesn't say much about whether it's true, but beliefs inform actions and actions have consequences.
If people believe that a deity wants them to do something, you (or others) may very well suffer from the consequences of that, regardless of whether that deity exists.
Many objectionable positions on modern social issues are arguably heavily influenced or determined by religion (such as positions on LGBT rights, climate change and abortion).
In this sense, if a particular deity doesn't exist, it would be important not only to establish this fact, but also to try to convince others of this (at least, if you care about preventing harm to yourself and others).
* People frequently try to make the case that religion is a net positive on society. But religion certainly doesn't have a good track record in that regard. Although that's an entire discussion in and of itself. In any case, if you do consider religion to be a net positive, you presumably wouldn't care to talk others out of it then.
How important you consider these "important questions" and to which degree you consider it to be something you "should" investigate are, of course, subjective judgements.