My still-new-to-me 28 Skater has a trim button on one of the Latham throttles, as well as two trim buttons (port and starboard engine) on both driver and throttle man side.

I am not used to these fancy vessels with more than one engine.

It looks like there are three trim diodes between the button on the throttle and the port and starboard buttons: green (in), blue (out) and red (power) . Not sure why red would need a diode.

When pressing the trim buttons, the following happens:

Throttle trim out: both engines trim out (as expected)
Throttle trim in: nothing (well, every once in a while, both engines trim in)

The buttons on the driver and throttle man sides behave the same way:

Port trim out: both engines out (I would have expected only port to trim out)
Port trim in: port engine in (as expected)

Starboard trim out: starboard engine out (as expected)
Starboard trim in: starboard engine in (as expected)

Questions:

1. Is the port trim out button trimming both engines likely caused by a bad diode on the blue wires?
2. Is a bad diode a likely cause of the trim-down button on the throttle not working, or should I look elsewhere?

Ive never really seen an intermittent diode...they are either working or not... Ive seen them shorted so the one way action doesn't work though......the throttle trim "IN" switch is probably going bad or has a bad connection somewhere since you say it works sometimes...
The port trim out switch would take some digging....either a diode is bad (installed wrong) or there's a short somewhere causing both to work instead of only one....

The switch in the Latham throttle has a short.
I have Latham controls and had to replace mine for similar issues years ago. The switch was just siliconed in place on mine.
Call Latham and order a replacement. The switch was like $25, but they would only ship COD and that was like $35, but that was years ago.

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Called Latham. The switches are $55.82 now. That is 82 cents for the switch and 55 dollars of value-add.

They accept credit cards now, though, so shipping to California is only about $16. (Shipping to Sweden is $132.94)

How did you disassemble the throttle handle? I removed the screws, but that was not enough to make it come apart.__PRESENT

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Do you think both "no trim in from the throttle" and "port trim button trims out both engines" have to do with the switch in the throttle, or just "no trim in from the throttle"?

it takes 4 diodes to make twins to work properly
so only 3 there is something going on in the wiring
red is power
blue is up trim
green is down trim
2 diodes on the green downs from throttle switch to each trim switch on dash
so both trim when hit throttle switch but 1 way power so when hit dash switch only 1 moves
that what the diodes do is 1 way power to keep the trim pumps seperated
then of course 2 diodes on the blue ups
so if hit dash switch and both move believe its a wiring configuration issue
the switch is hard to replace on them throttles and can be the switch if dont go up or down when hit switch
but both moving at throttle and at dash switches and only 3 diodes prob a wiring issue

Sorry if I was unclear. It is probably 3 diode kits each consisting of 2 diodes, not 3 diodes. Hard to know what is hiding under the black shrink tubing.__PRESENT

I missed that part in your original post.
It could just be a wire that is connected to the port trim button that should be connected somewhere else.