The tach tends to wobble a bit more than the speedometer on our bikes. They are held in place by just a single arm bracket and this tends to weaken and break, giving the tach that droopy look. You might check the bracket mounting inside the insturment cluster to see what condition it is in. Some have fixed it with JB Weld, or re-enforced it with a washer.
I added a brace between the speedo and tach with a piece of brushed aluminum L bracket. Just drill the holes in and use the existing screws from the back of the buckets. Also provides a handy spot to mount a clock or voltmeter!
Patriot Guard Rider
2000 VN750 Sere (Serendipity)
1990 GL1500 (Ole Blue)
1986 VN750 EVie (project bike, heavy custom)
VROC # 11628 / 25000-H
ARVROC # 12 Coordinator and Crowd Control
OKVROC # 18 (H)
TNVROC # 45 (H)