CA213C is the model number. The later models, starting with The 2600, 3600 and 4600 series in 1976 and onward, aren't documented as well on the internet as the 1965-1975 2000, 3000, 4000 and 5000 series. The C is definitely a "3000" series, and I believe that the A makes it a 3600, and I think that the 2 after the A makes it a "highway chassis" version of the 3600. The 1 means that it has a diesel engine, and the 3 means that it has live PTO, and the C at the end means that it has an 8 speed transmission (4 forward and 1 reverse speed on the main shifter, plus a separate high/low shifter)
*B294478* is the serial number. The B at the beginning means that it was assembled at the Basildon England assembly plant. The Basildon (B) and Antwerp (A) serial numbers aren't documented as well as the Michigan (C) serial numbers are, so it doesn't help much in narrowing down the year, but the 3600 was only made from 1976-1981.
6M6 is part of a production code, which should tell you when the tractor was assembled. The first 6 should be the year, which would make it 1976, and the M would be the month, which would be December, and the second 6 would be the day of the month, so your tractor was assembled on December 6, 1976. There is usually another letter, A B or C, at the end which would tell you which shift did the final assembly, but that last letter does seem to be missing on a lot of the A and B serial number tractors.
So it looks like you have a highway chassis version of the 3600 with a diesel engine, 8 speed transmission and live PTO that was assembled on December 6, 1976 in Basildon England.
I have a Select-O-Speed transmission with independent PTO on mine, so mine is nothing like yours, but from what I've read of others experiences with the live PTO control linkage, it shouldn't be too hard to open it up to see what the problem is. In looking at the New Holland parts site, it may just need to have the pin replaced that holds the PTO control handle to the shaft that goes through the side plate on the transmission. Since that's on the outside, it would definitely make sense to check that before you open anything up.