Jim Kaufeld writes:

First verify that your engines are sufficiently grounded. Then
verify it again. Check your alternators while you're there.

What, exactly, should I check?

I'm not sure of the proper way to test, but there should be (next
to) no resistance between the engine and the airframe.

I would have assumed that since the starters
work on both sides, the engines are sufficiently grounded.

It seems reasonable to assume that but it is definitely not
correct. (I was a counterexample.)

(Incidentally, not long ago I really toasted some wires on a
grain truck upon starting it because its ground cable was loose.
It had been starting hard for awhile, but when the cable really
went, the starting current took another path, through a small
auxiliary cable. *Poof*)

Is there typically
a separate ground that goes to the engine? Should I add one?

There should be a big strap from the engine block to the engine
mount. The rubber cushions of the engine mount electrically
isolate the engine but there are probably other things that
provide a path to ground. Even a ground strap can become
ineffective (as in my case - corrosion, I recall).

Next see if you can isolate a bad probe (or probes) by flying with
some disconnected.

One thing I've noticed is that when the GEM is working the CHT on the RE, #2
varies. I figure that either something is wrong with that probe or the
connections to the probe. Can just one badly connected probe -- or maybe a bad
probe -- make the whole instrument dance?

Yes. It happened to me. (I had multiple problems last time.
That made the diagnosis much harder.)

The probes seem to die much more frequently than I'd like. I
recommend getting some extras to carry.

Thanks for the help.

You are welcome. I hope you solve it.

--kyler