Yes, there indeed is an oil pump on the inside face of the timing cover:
It is a 3-stage pump. I have not traced the passages specifically on a F/G31, but if it is like other 3-stage Douglas pump circuits, and referring to the following image with the pump removed...
...the oil from the tank enters the fitting at the front face of the drip sight plinth, enters the smallest pump stage (to the right) and is pumped to the drip sight bib.
It is then drawn from the drip sight bowl by the middle, next larger stage, and pumped to the quill feeding the end of the crankshaft. The quill is missing in these photos.
After doing is job in the engine, it drains down to the sump under the crankcase and is drawn up via a drilled gallery to the third, and largest stage of the pump (left end). It passes out via a fitting in the front face of the timing cover, thence to the oil compartment in the petrol tank.
Possible failures are the paper gasket between the pump body and the airbox has blown out. The drive gear or worm has stripped, The peg has broken off the rides in the gear cam track so the pump is rotating but not reciprocating. There is also a bypass in the pump that passes oil above a certain pressure (as restricted by the needle valve in the drip sight) from the exhaust back to the inlet port of the 1st stage. These generally do not give trouble, but it is possible it is stuck open or the spring behind the check ball has corroded from acidic oil and failed.
The oil is collected from the sump and returned to the tank. I have not had one of the sump plugs out, but suspect (again) if like other Douglas systems the cap has a wire screen soldered to it to filer out the larger debris before returning the oil to the tank. This screen could be sludged or gacked up, but that would only impact the flow of oil back to the tank. You ought to still be seeing oil being pumped into the sight glass.
Likewise you could have a failure in the gasket under the drip sight bowl allowing it to suck in air, but it still should pump oil to the drip sight.
There ought to be a screen in the fitting in the bottom of the tank that oil is drawn from. That could be sludged up and would be the first and easiest thing to check.
Some of the drip sights have a one-way ball check in the drilling for the needle valve (from underneath), but I do not know if the F/G31 is one of those.
-Doug
