Sir ben_nexus
In your photo submitted, your potential faulty Electrolytic caps units are typically going to be the two LARGE ones near the 4 screw terminals at the rear end.
The gold stripe down the side is marking the negative terminal /lead of each unit.(Suspected as 2200 ufd @ 35VDC by the two singly visible numbers on cap ends.)
If being MY my unit to test . . . . .I would connect up just enough of a load to get the unit turning on and off / pulsing, as it was.
Then get / find yourself another new or even . . .suspected / assumed as good . . .test capacitor . It can be even less than that units marked capacitance,( say 1000-470) or more, should you be having a problem of EVEN having an electrolytic capacitor on hand, or it could be be temporarily cannibalized from some available other electronics. Be SURE it has at least the same voltage rating as the installed big caps or even a bit more.
Then, if finding yourself having a short leaded test unit, tack on some temporary extender wires and OBSERVE THE marked / + and - WIRE POLARITIES and then touch the " new " capacitors leads across one of those mentioned big electrolytics to see if the power pulsing does not then completely stop, or at least, get slower. Try that on both caps, one at a time.
If no good results, move to the MUCH smaller orange cased unit at center chassis, it being of much less capacitance , and possibly marked as having a lower voltage rating. You then need to find another test cap at or close to its marked on cap and voltage specs .
If no luck, then the last test would be for the two LARGE E-caps that have yellow tape across their tops.
A potentially simpler test for them would be merely using a DVM in its DC volts function and set for a voltage range of being more than the voltage rating marked on THOSE E-caps and initially have no load on your output terminals and be reading the voltage across those E- caps and commit the voltage read to memory and then connect the load and see if the degree of voltage dropping mimics the power supply's pulsing output.
I really think that the earlier caps would be the problem . . . . time of use and their eventual deep capacitance decline, down to the depleted storage capacity state of their now telling you . . . . " I can't . . .KEEP UP . . . and take it ANYMORE ! ! ! ! " . . . .so they are now just working in " built up bursts" .