I have completed this testing as well and I do see ROUT drop to 0V when RIN is 5VIf all the voltages are correct as I have given,
1) with no signal at R1IN, what is the voltage at R1OUT? It should be 5V.
2) with R1IN at 5V, what is the voltage at R1OUT? It should be 0V.
You nailed it, PC ground was not common, serial adapter ground was 5, was using 7, corrected this and all is working. I cannot thank you enough for this guidance. It is very much appreciated, and I have learned a lot Thank you so much.From what I observe, your GND connections are not consistent.
Check all GND connections
PC GND
Arduino GND
+5V supply GND
MAX242 GND
Oscilloscope GND
Check those grabber hookup jumper cables. They often go bad.

You are very welcome. Glad you found the problem. Never discard the thought that it is a simple problem.You nailed it, PC ground was not common, serial adapter ground was 5, was using 7, corrected this and all is working. I cannot thank you enough for this guidance. It is very much appreciated, and I have learned a lot Thank you so much.