No start after cleaning up wiring.

You are the umpteenth kid who wants to "wire in a push button." In the length of time, trouble, and cost that it takes to wire up a scabbed in PB you could troubleshoot and find out what is the real cause

You have a shop manual? Download one here for free

http://www.forabodiesonly.com/mopar/showthread.php?p=1970088617

Somewhat usable but not always complete manuals here at MyMopar:

http://www.mymopar.com/index.php?pid=31

The start signal comes from the key (yellow) runs through the bulkhead to either of the push-on terminals of the start relay.

So make sure you have voltage there in "start." If not, go to the switch connector under the column and check on both sides of the switch connector. If you do have it there, but not under the hook, it's trouble in the bulkhead connector

There is however a MISPRINT in the 72 shop manual.

The wire to the starter relay seems to come from "T" of the bulkhead, "dark green" but is probably YELLOW and go to one terminal of the relay. You should be able to SEE that wire, so if the manual is wrong you can quickly sort it out. I believe "L" is the horns

The second "push on" terminal of the start relay goes to either the clutch safety switch or the neutral safety switch depending, and is grounded when in park or neutral, or with the clutch depressed.

Those two "push on" terminals of the relay are the COIL of the relay.