Yes... if you stick a meter in the power plug... you should see 12v when the power is on.
Checking the pulse is a little more difficult, but a "Cheater" way of doing it is to put the positive wire from your meter into the plug, and the black to a ground source. You shouldn't see any voltage. Once you start the engine, you should see some AC voltage. (or a DC pulse) The actual number isn't important... but you should see a change from stop to running.
If you have an O-scope, or frequency counter, you can actually check the pulse.
Finally, yes, #35 is it... but I'm sure you could find a tach for a fraction of the price on eBay. BUT... I'm sure you are going to find that there is an issue with the wires. The tach's almost never go bad... and when they do... you will see condensation in them, or the needle will be stuck mid swing. (the bearing shattered)