If it's just the tach, and the symptoms change as you change the load on the alternator, then there's a good chance the problem lies with the alternator itself (since that's also where the RPM signal is coming from).
I've seen this movie once before and the issue was the alternator was starting to give out... not so much that the battery didn't stay charged, but enough that the tach output was flakey. A voltmeter on the alternator might be a good next step, particularly if you can watch the alternator output when the tach misbehaves.
Having said that... if the cluster itself shows any other strange behaviors... specifically if the speedo starts to misbehave as well, then the problem is 99.99% of the time a dying cluster and replacement is pretty much the only option... no user-maintainable parts, no schematics available, and it's never ever just a ground or solder connection. Ever. :wink: