You could test a thumbwheel control using a DMM, but this is tedious and time-intensive. A great solution is the thumbwheel tester. Although you may be able to build one from a schematic, it's probably more cost effective to purchase one from a thumbwheel control manufacturer or other source.
Anyone working in binary logic is familiar with truth tables, which show you all possible outputs corresponding to all possible switch positions. Use the tester to show the results of toggling each thumbwheel switch; compare each output to the truth table.
As you test each switch, you simply have to find a result that doesn't match the truth table to see that the thumbwheel control is bad. If all positions check out, the control may still be bad. Watch your tester to see if any LEDs flash when a switch is between positions. If you get that behavior, replace the bad thumbwheel control.
If the thumbwheel control passes these two tests, the problem is in the wiring rather than in the thumbwheel control.