I would have a few questions:
1) Define momentary
a) Like a 10 millisecond push/edge trigger -or-
b) Hold button, and in 3-5 seconds it turns on.
Aside: I know you said momentary, but you also said switch it on. Your NOT looking for something that uses a on/off switch, but delays the power 3-5 seconds?
2) Define the current at 12V
4) clarify 2.5 cubic inch rule
a) If a relay was used, does the 2.5 cubic inches include it?
Aside: Solenoids don't "open" unless they break. They may "pull-in" or "activate". The solenoid could "open something" like the trunk.