Quite welcome, just quick napkin scratches w a bit assumptions on the boat. Takes the guess work out though........
Your idea is neat, I like it and your thinking outside the box, it's quite founded IMO, similar to having a steering position indicator, nice to know where things are at a glance, engine/key on running or not, esp with a system that has power to the trim motors w/o key on, running blind (or being able to, is this stock?) isn't too good and isn't a good design IMO............No main switch? Wow, hmmmm, ummmm, I'd definitely consider installing main batt. switch in the future.....Dog butts/kids sitting/bumping on switches controlling outdrives on the trailer and at the ramp? Stranger things have happened......
The work around? Not too complicated at all!!.........A standard SPDT relay (prevents other loads from coming on with the trim gauge) and a OR'ing diode config (two diodes, D1, D2 wired as shown) with the trim switch up/dn relay control signal will do what ya wanted w/o a main switch.........It's basically Silver's idea, with the key still off, the gauge will work only when either the up or down is used/bumped. It'll work as normal when the key is on/motor running. You could use a push button tied to the batt + to activate the relay when needed and skip the diodes as an additional option.
Not sure I can see/in-vision the config as suggested where just a diode/s would be installed and still prevents the other ig. loads from being turned on at same time. And, in addition to leaving the gauge tied to the ig. so it works with motor running (sketch would help).