Well, I would ask if it's a 7201 or 7203, but I think the color processing and neckboard circuits are similar enough between the two.
No red can be diagnosed as one of the following problems (in order of start to finish through the monitor):
1) no red signal detected from the PCB, either due to bad video output or a wiring issue.
2) Bad solder joint on the red pin of the video input connector.
3) no red voltage input to color processing IC (bad parts or traces between input pin and IC)
4) no red output from color processing IC (bad IC)
5) No red voltage at connector output to neckboard (bad part or trace between IC and output connector)
6) No red voltage at neckboard connector from chassis (bad wiring or connector)
7) Bad red adjustment (pots)
8) Bad color drive transistor
9) bad solder at red pin of neck socket
10) bent or broken pin on the tube
11) bad color gun inside tube (test with rejuvenator)
You can save some time by checking #6 first. If you have voltage there (same as blue and green), then you go down the list. If not, then go back to step #1.
And I'm tired, so I might have missed something...