If you rev up the engine with the bike sitting still, it still behaves normally?
If so, and it only happens when moving, then it is an intermittent connection - but it could be inside the tach or in the wiring to it.
The black plastic covering piece can be a bit daunting to remove, but it isn't that difficult once you've done it a few times. The only tricky bit is dealing with the little plastic tabs that clip on the front leading edges of either side, on both sides of the headlight - but 90% of the time, one or both of those are broken off over the years anyway.
My wife has my camera, so I can't take some guidance pics for you, but will try to describe:
1. IF you have the black plastic interior fairing covers (these are black plastic-obviously) pieces that fit around the top of the fork tubes between the upper and lower triple clamps and cover the space behind the painted wedge fairing, on both sides. There is a single screw at the outer corner of each one that screws into the painted fairing piece. These must be removed first. To remove, - remove the screws, and carefully work the plastic piece back toward the rear of the bike - it will flex some. IT is curved around the upper fork tubes, so you want to gently work it back from around the tubes. Be patient, they do come out - you might have to loosen the throttle housing/master cylinder clamping screws on the handlebar to allow for more wiggling room, especially if you have the low, Euro handlebars.
2. Once those pieces are off (or if your bike doesn't even have them) you look for two small bolts up near the top of the space inside the fairing on either side of the instruments - you will see that the bolt holds together a black plastic tab from the black top cover and a slotted tab from the painted fairing cover - remove (or at least loosen) bolts on each side.
3) Take a set of circlip pliers - or a suitably long and pointy set of long nose pliers can do- and put them into the (2) holes in the metal ring that is around the ignition keyswitch. Unscrews the ring and remove it along with the plastic ring that is under it.
4) Now for the fun part - to get the black plastic piece off, you need to gradually work the black cover both upward (from the ignition key end) and backward (sliding from the front edge near the headlight). It will want to grip the rubber seals around the instrument dials - just keep working it gradually up and to the rear. There are (2) small hidden "clips" on thepainted part of the fairing toward the headlight on either side which are intended to grap onto some plastic tabs which or on the underside of the left and right edges of the black cowling cover. You *may* need to look under there and carefully release the tabs if they are reluctant to let go. These things are broken on most of these bikes, but if you still have yours you will want to try to keep from breaking them off. I just keep gradually working the black cowling a bit upward at the rear and sliding it back a bit until the rear is clear of the instruments and it comes smoothly off.
Now you know why those tabs are often broken. this is also the only PITA part of working on the R65LS models, IMHO. Now, you can see the back of the instruments and access the connector/plug on the tach. somewhere I have some pictures concerning taking the tach apart, but it sounds like that might be beyond what you are willing to venture into. In any case, you will have to go through all of the above to remove your tachometer to send it in for repair if you don't find an issue with the wiring or the plug.
Best of luck!
NH Mike
