I am not an expert on servicing the R2001B which is an almost entirely different animal than the D version which was the last to be released. But the main point is that only the D version did fix many well known issues that where prevalent in the earlier A-C versions, including the elimination of the somewhat flimsy front swing handle. Another issue with these monitors is that the early ones had Magnavox CRTs that tended to get weak and fail way too soon. For the D series Motorola started using imported AEG and Telefunken CRTs that performed much better over time, but given the age of these instruments now, one should always check that the CRT is still good no matter what version. And once the CRT goes bad there is no easy alternative but to find a replacement ("unobtanium"), try using a CRT restorer to restore some of the life in the CRT, or jury rig an external XY monitor. Without a working display the R2001 is basically useless.
So my only advise in this case would be to start checking all power supply voltages BEFORE doing anything else like swapping caps etc. And for anyone else out there looking to get one of these R2001 service monitors to ideally always shoot for a R2001D, and even better if its a HS variant (high stability main oscillator).
There are many variants of the R2001D with slightly different model numbers depending on options like cellular, encryption, trunking, etc, but the desirable radio testing base capabilities are always present on all of them. One of my service monitors is a R2008D-HS, which basically is a R2001D with an added card for analog cellular testing. When I got it it had a few problems like a flaky tuning encoder ("RF Scan") and the PL/DPL tone generation was not working. Was lucky enough that seller had lots of spares on hand and send me a replacement board to fix the tone issue (was a bad crystal), and also a working rotary encoder.
Randy.AB9GO