Voltage problems, cutting out when hot

Red J1 on the new switch has 12.63 constant (same as battery) with key off and nothing else has power. When key is on yellow S2 and blue J2 had 12.00 volts.
I was just trying to show the voltage differences between the old and new switches, doing nothing else but changing switches. (Even if the voltage readings are still wrong, at least they are moving in the right direction)
Something must be connected.

Everything off (including dome light) and we see maximum battery voltage. It's like an air compressor tank that was filled. We can check the pressure on the tank itself, or we can check at the remote filter. or end of a 100 foot hose. Pressure at the end of the hose is same as the other two locations.

When the key is on, current flows through the ignition points or amplifier, and it is flowing through the voltage regulator - rotor circuit.
Measuring at the middle of the feed for those circuits, the 12 volts you see could be true battery voltage under load. We don't know.

Lets look at this on the schematic used earlier.
Arrow is your meter's red probe.
Voltage at that connection will be battery voltage.
upload_2019-8-11_7-27-21.png

Turn the key to Run.
Current flows through that connector to the switch and then thorugh the rotor, the ECU, and some through the coil.
upload_2019-8-11_7-44-11.png
If the voltmeter black probe is touching a chassis ground, then the voltage at the arrow is battery voltage less any drops due to resistance in the circuit up to the red probe, and any in the ground after the black probe.
upload_2019-8-11_7-46-52.png
We could assume the battery voltage is still 12.6 Volts; and we could assume the ground connections are perfect.
In we case we can conclude there is a 0.6 Volt drop between the battery positive and the probe.
But we don't know that for sure. Better not to assume those things.

One check would be to measure the battery positive to ground under the same condition.
Another check would be to measure voltage drops directly along the flow path.

So if we saw this.
upload_2019-8-11_7-57-50.png
Then we know there's little voltage drop in the wiring up to the connector.

But if this,
upload_2019-8-11_8-1-0.png
Then maybe there is resistance in the wiring, but it could be in the ground connections.

Then measure drops directly.
(If using an analog voltmeter, or your DVM probes don't handle reverse you'll have to put the + probe on the higher voltage location)
upload_2019-8-11_8-6-39.png

.3 V drop under 5 -6 amps isn't great but IMO isn't terrible.

Should get about the same reading at the welded splice.
You can measure that using the alternator output wire as a probe extension because there's no current flowing in it.
upload_2019-8-11_8-14-18.png