Rules and Prioirty for Inter-Squadron Aircraft Scheduling

Can a current CAP pilot  book airplanes based at or belonging to other squadrons in your wing?   If so, is it on a first come, first serve basis in the WIMRS scheduling model or are there other protocols to follow with notifying the other squadron.   (Trying not make an assumption/mistake.)   If so, outside of actual rescue missions, what types of flights have priority over others.

Yes.  Units are the stewards, not the owners of COAs.

FCFS.

Scheduling procedures and POC notification policies vary by wing.

Beyond that it's at the whim of the Wing, usually the DO,
with any number of competing priorities, some that change urgency based on the time of year.

O-rides might win over a sarex if the Wing CC has decided that's his emphasis, all may lose out if your wing is "lucky" enough to host an academy or contributes aircraft to something NESA.

Etc. Etc.

Obviously you need to work with "someone" at the other squadron. You can't just simply schedule in WMIRS and then show up ready to fly. You'll need gate access to the other airport. Keys or combinations to the hangar. Etc., etc. So you'll have  discussions with a pilot in that squadron, seeing when your available times can match up so he can meet you there. THEN, you can think about WMIRS.

We have a 172,  but we will a couple times a year, swap planes with another squadron, so we can get some 182 proficiency time in, and then do our Form 5s in it, so we are covered for both. Your squadron may want to consider doing something like this, if you are wanting to fly a different plane.

We did the same thing last year with a squadron that has a Maule. Swapped for a couple weeks so we could all get checked out in it.

(And of course before people jump in here .... getting checked out in a Maule doesn't mean you are proficient with one, etc., etc. But you have to start somewhere. )

You can't just simply schedule in WMIRS and then show up ready to fly.

There are plenty of places where this is all worked out well in advance, aircraft are at public airports with no special access
needed, Keys are in a combo box or with the FBO, and yes, in fact, you can just schedule the aircraft through the national
scheduling system and go flying (obviously you need a release).  POCs are expected to be checking their emails and WMIRS
and be aware of who and when the plan has been reserved.

The process however, is decidedly local, with some wings still allowing POCs to require a ritual sacrifice, 3 forms of ID (and the pilot has to be tracker-chipped),
with advance notice in excess of 2 fiscal years, but that's not how it's supposed to work.

... aircraft are at public airports with no special access
needed,

Yep it varies.  We have codes to get through the gates here, and the airport authority is about to change to an ID Card system for everyone needing access, that will have a barcode or similar to scan.  SO unless someone is with you that has a card, you'll not get in. I'm sure all our squadron members will not have a card, but trying to make sure all our pilots will have one.

From experience, our Wing has procedures in writing how to go about "borrowing" another squadrons aircraft. Not complicated, just requires advanced coordination/scheduling.