How can I find the S1 of my unit?

Well....depending on where your unit is located....you have either 1) A unit ARA only; 2) A unit ARA and an RPAC (Reserve Personnel Action Center); or 3) A unit ARA and BN or BDE S1.

It really all depends on where you are at and what type of Reserve Center you are in.

But, for starters, begin finding your unit ARA.

Please tell me this isn't a case of NCOs failing you by telling you to "figure it out" on your own?

You can reach out to your ARA (Unit Administrator) as they are the primary personnel action POC at the unit level. Make sure to look in your NCO Support Channel so they are aware of the need and they can likely assist you.

Call Bn HQ on phone and ask for S-1 shop or ask your AST.

What is the Unit name, and where is your unit located?

If you are in 702 EN CO, they have an ARA (the S1 would be at the Battalion=844 EN BN). You ARA should be doing the same work as an S1.
The S1 is typically AGR who rotates out just like active duty, so it may be difficult to track down a physical person (unless you talk to someone in your unit).

I've noticed the reserve admin is much more haphazard than active or guard so I'm not shocked no one knows who the right person is.
What unit are you in / what is the location of your reserve center?