Well, I think that you make a good point there. Let's start over.
I had you looking for power at the fuse block because you initially said that you had power to the 150A fuse. BUT, maybe the problem is much more simple in an "electrical circuit" sense. So, let's go back to basics....which is where I should have suggested from the beginning. This may be (probably is) a simple bad connection from the battery.to SOMEWHERE on the outboard. Corrosion is quite often the issue....especially in the marine environment.
I hope that you understand that, in an electrical CIRCUT,....(meaning circle)....
the ground connections and wiring are EQUALLY as important as the "positive" connections and wiring. We often get tunnel vision when looking for "power" in a circuit and focus just on the positive while ignoring the ground connections. That's what I did here having you looking at the fuse block. GUILTY and I apologize.
The tilt motor gets it's power from the tilt relay which is powered DIRECTLY from the starter motor stud via a white wire. IF the stud is getting voltage but the tilt doesn't work, it's highly likely that it's due to a poor ground SOMEPLACE.
So, let's take a measured approach and start checking BOTH positive AND negative battery connections starting at the battery and main cables. Remove both cables from the battery and check your battery voltage. If 12.4 volts or above, ok if lower than 12.4 volts, I would charge the battery and have it load tested just to be sure.
Thoroughly clean both cable clamps and battery posts. If you have a 1-2-both switch, remove those connections and clean them all.
With the battery or batteries disconnected, (and this is where you will start to hate me) remove ALL wires connected to the starter motor stud and clean all of those.
Here's where you will hate me even more...
...find where the main battery ground cable connects to your outboard. Most are NOT in an easily accessible place. Remove that connection and clean the mounting surface, cable eye, bolt or stud and all other wire eyelets that may be connected there.
Make ALL connections SHINY. It usually takes more than one size wire brush and maybe a battery post cleaning tool too.
If your battery tests good and everything is cleaned, put it all back together and try it again.
While this is for sure a real PITA, it will give you a solid base to start testing from if the system still gives you trouble.
In the meantime, between wire brushing and repairing nicks and scrapes to your hands and arms, Google "voltage drop testing" and bone up on that. It's absolute MAGIC for finding and solving electrical problems if you make the effort to read about it, maybe watch a couple of videos and then try it.
And, while for much of my career as a fleet truck mechanic there really were almost NO short cuts to doing electrical troubleshooting, volt drop testing IS TRULY a good one.
Hope I'm not boring you.