Simple test. Disconnect the cable at the drive unit at the wheel. Spin the cable using a cordless drill and bit that will make it spin. Do both forward and reverse just to be sure. If the speedo works, then it's your drive unit.
The plastic gear on my 1100 cracked and I had to get another used one last week.
Not sure on your 1000, but my tach runs off the fuel pump. I'm ass-u-ming you can do the same procedure but I haven't done it personally.
The procedure for testing the speedo is correct. But there is one more common problem. Inside the wheel is a small drive unit (looks like a big washer with ears on it) that the outer drive unit marries up to. This is notorious for failing. It is only like $6-$8 from Honda and easy to replace by pulling the front wheel.
The tachometer should also run off the fuel pump on the 1000. It is the same on my 1100. You can disconnect the cable from the back of the tach and run the engine. If the cable is turning it is the tach itself but most likely the cable is bad. Another common problem with the older bikes.
At home I have some pics of the speedo drive I am talking about. I will try to upload them when I get home.
I also have a tach cable available on eBay that I am selling. It is item # 150363127551 and at 9.99 plus shipping.
I had the same problem on my 77 gl1000, pulled the drive off the front wheel and found the drive part with the ears wasnt meshing with its mate. Pulled that part out and put an o-ring behind it and away she went, still working 1000 miles later. Will do a parts replacement later. Cheers Tunnow