Brake cleaner will get things bone-dry, so what you are hearing is metal-to-metal rubbing.
There should be a film of oil between all the moving metal parts--Rocker shaft and rocker arm bearings, rockers and valve stems, etc.
Not sure what you mean by "gunk around the valves"--I'm guessing that you mean valve stems. The valve stems are on the inside of the valve springs and should have seals around the stems to prevent oil from entering the combustion camber via the valve guides. The bronze valve guides do not require lubrication for smooth operation, but if you somehow got brake cleaner past the seals and in between the valve stems and the guides, that could cause squeaking and potential seizure of the valve. Not sure what you'd have to do about this.
As for all the other bearing surfaces, you might squirt a little engine oil in all the bearing holes on the rocker arms and add some to the ends of the valve stems and see if it helps till engine oil pressure can make it's way back up there (presuming you have any oil pressure like Stomper says).
--Mark
1973 SIII 109 RHD 2.5NA Diesel
0-54mph in just under 11.5 minutes
(9.7 minutes now that she's a 3-door).