So I have had good luck with reviving old stamped numbers on old tools. Take some white chalk and rub it into the numbers real hard. Then wipe off the residue with your fingers, it sometimes leaves an impression of the previous, hard to see, numbers. Also having an oil cooler is not a bad thing, military cars had them due to the number of hours the engine was running. Low miles, high hours on the engine. But your description of the gauge and sender is funny, someone did some hack there.
I tried the chalk and the best I can come up with is 2543633 and possibly a 0 or 8 as the unreadable digit.
This link explains chassis numbers. Seems like only the first 3 digits actually mean anything.
https://www.lrfaq.org/FAQ.3.Chassis_Numbers.html
According to it my chassis is 1962 or later.
As for the oil cooler I probably didnt explain things to well as it looks completely stock. The broken line from the gauge ran around the drivers side fender well to the oil cooler line. I removed it and I installed a new oil temp gauge. Pic shows where its connected.