Don't know your vehicle but judging from your handle you might have an oval bug. 6Volt? If so, corrosion at the fuse and loose connections and corrosion at the screw on wire terminals are your greatest enemy.
It would be nice to have a digital voltmeter to see if any power is moving around the wiper system.
Start with the fuse box under the hood and check for corroded terminals and fuses. I believe the wiper fuse is on one side of the fuse box. Can't remember which side - last oval I had was 20 some years ago. Clean, clean clean using sandpaper or a sharp knife. You want a good clean connection.
You might just want to disconnect the negative battery terminal so as not to short anything out while cleaning particularly if using a knife or metal object to scrape away the corrosion. If the fuse is badly corroded, replace it.
Check the wire from the light switch to the other (hot) side of the fuse for tight and non corroded connections. This fuse gets its power from the light switch.
Trace the wire from the fuse box to the wiper switch and wires from the wiper switch to the wiper motor. There are a couple of different configurations depending on whether you have a self parking wiper motor or not - one additional wire to check. Again clean if required and tighten the the screw connections everywhere. Hopefully you will be able to get at the screw connections without removing the wiper motor or switch.
Check to see if there is voltage across the wiper switch as well - when you pull it out and ignition key on, if I recall. Oh and after you reconnected the battery.
This should get you started. I'm sure some of our learned members will chime in if I've missed anything.
My thoughts for now!! Sun is now out - got to go play!!