I don't see how there could be any time lag in the hydraulic system, unless you had a very restricted line and there was air in the line. But I think you would already have other problems if that were the case.
This is an interesting problem, so I guess congratulations are in order for coming up with it! :thumbsup:
If you have a good multimeter, maybe a next step would be to disconnect the wire from the back of the trim gauge, and measure the resistance looking back into the sender as you change trim. That should isolate the problem to either the gauge or the rest of the system.
I think you will find that the trim sender wire color is brown. In my boat, and probably in all, the sender is considered part of the engine/outdrive. So it is part of the wiring for same, and interfaces to the boat at the large round connector on the engine. This connector has quite a few wires that head towards the helm. So the wire should enter and exit the engine harness connector as a small brown wire.
From the engine harness, it should make its way to the helm. There is probably an instrument cluster connector at the dash that heads back towards the engine hardness. The wire should be brown here too, and go to the trim meter. So you could lift the brown wire from the meter, and measure the resistance from the brown wire to ground as you vary the engine trim.
If you go to
this page, and scroll down about half way, you will find three small photos side by side. Click on the picture of the instrument cluster, the middle photo. It should bring up a schematic of my instrument cluster. Yours should be similar.