Well, it'll be hard to sort out remotely. It's not stock, there is no electric pump in a stock 81, plus the fusible link issue plus who knows what else.

the starter only needs two connections, well three but the third is via being bolted to the engine. You have one fat cable from the battery + and a smaller wire from the starter relay. The small wire from the relay is what tells the starter to turn over. For that relay to work you need 12v from the ignition switch AND a ground thru the neutral safety switch. Did you happen to knock off there connector at the NSS? Put a meter on the starter relay and see if you are getting the ground and check the 12v in start as well, need a helper as well.