Been a while since I posted here, but having restored a Pioneer SA-8500 II, thought I'd chime in. Some great suggestions so far.
The thought of a dirty switch is a good suggestion, however, this unit does not have a rotary selector switch - it is all push buttons (pushing in one source pops out the currently selected source). See this pic of the 950 (its a beauty): https://www.classicaudio.com/forsale/pio/SX950.html
Trying out the phono2 input to see if it has the same problem would likely determine if the problem exists on the switch board. All of these switches (rotary and push button) need to be cleaned in a restoration on these older units (and not just by spraying deoxit all over the place - they need to be pulled out, taken apart if possible, crud cleaned off, and the appropriate contact cleaner/enhancer applied).
Also try connecting the turntable RCA leads in reverse (left to right and right to left) and make sure the sound in the right speaker still goes out. If the left channel goes out in that case, then the problem is before the 950 as @elliottbnewcombjr suggested - either the RCA connectors, the cables, or the cartridge leads or the cartridge are the issue.
If it is not one of those, then it is could be something on the phono stage itself - the phono stage in this unit is very simple and uses six transistors, all of which are known to fail eventually. They have readily available and easy replacements too. This fellow on audiokarma had the same problem and fixed it by replacing those six transistors:
https://audiokarma.org/forums/index.php?threads/pioneer-sx-950-no-right-channel-on-phono.1032652/
If you end up replacing the transistors, might as well replace all the electrolytic capacitors too on the board as well while you are in there.