You are missing the original faucets. You can still buy one of the hand pump faucets, they are used on pop-up campers. Amazon has them.
Of course, the old plumbing will be very suspect and IMHO, should be replaced with PEX before you hook up to water.
Trilliums have commonly known issues that many have addressed before you, including belly band
leaks,
window leaks, body to frame bolts, hinges that attach to rotten wood.
The roof was not designed to support roof air. You are going to have to come up with a support plan there.
Trillium did have a roof air option, but it had a special designed roof section, much higher than the rest of the roof. Pretty obvious if you have one. Your pictures don't show the complete side profile, but I don't see that roof section. Even supporting a Maxxifan (roof vent fan) takes extra support.
You got a good one! And Trilliums are really desirable (I own one so I could be biased...)
On these vintage trailers, water and
leaks are the enemy. You can have
leaks that start inside from plumbing leaks, then leaks that start outside (windows, belly band, every penetration through the shell). That top rail you have around the top looks like an add on. Watch out for leaks there.
When you get to that point, don't be in a hurry to hook up power. Depending on what your trailer has, the old power control centers are pretty bad, and need to be replaced.