The reason you cannot connect the gauge to the dimmer switch/ rheostat is because the gauge works in the reverse way -

when the white wire detects a 12v signal, the gauge dims, this is connected to the lights, it can only have 2 levels of broghtness, bright (for daylight) or dim (for night) it cannot have a dimmer or connect to the cars dimmer/ rheostat because of the design of the gauge/ the way it is wired

if you connect the white wire to the sidelights/ light switch the gauge will dim when you switch your lights on - i don't recommend connecting it to headlights / dip/ main beam or it won't dim untill you switch your main or dipped beam on (whichever it is (wrongly) connected to)

the confusing thing about this gauge is the fact that when a 12v power is connected to the white wire the gauge dims, and if this wire is earthed it stays bright ("daylight" mode)

If you connect the white wire to the sidlights/ main 0n/off light switch on the car (not the dimmer) the gauge should come on (brightly) when the cars ignition comes on and it should dim when you put your sidelights on (and stay dimmed when you put your main beam/ dipped beam on)

as before - it will not work with the cars dimmer
It may be possible to get your other gauges to match the way the Innovate gauge dims - it might look neater

i hate wiring cars too - and im an electronics engineer!

PS - you must connect it (the white wire) to a sidelight feed that does not dim with the cars instrument cluster - eg - the sidelight feed from the light switch