1979 Rolls Royce leaks hydraulic fluid from right-front brake circuit. It does this when simply parked with engine running, while operation of brake pedal has no affect (either way) on fluid drip. This makes me think it is the hydraulic pump for this circuit (each circuit has a dedicated pump). Is there a clever way for me to test this?
Put the Rolls on a lift and inspect the pump. Do you see fluid on the pump body? If so, you found the source. If not, follow the brake line to see where the leak is. If the pump is too dirty to tell, wipe it cleanand let it sit while running until you see some drops on the ground. Then inspect.
Why are there hydraulic pumps in your brake circuits? I don’t remember ABS being available on anything in 1979, except aircraft.
I think it is leaking hydraulic suspension fluid.
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Because it is a Rolls Royce. 
For OP. Maybe You can find something usefull here:
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If I am not mistaken Lockheed had a hand in the design of the insanely complex Rolls Royce Hydraulic brake and self leveling system. It is a nightmarish warren of pipes, hoses, pumps, sensors and hydraulic fluids. That are responsible for the brakes and the leveling system.
I’ve touched a few of these systems and I was able to repair some relatively minor issues… But that first encounter I recall quite well, I went home feeling like I knew nothing about cars or mechanics…I was lost and confused. I have since recovered at present however.
These systems are NO joke… You need the diagrams and layout of everything to even begin to have a fighting chance at handling anything. This is not beginners territory… Arm yourself well with information before going in…trust me on this.
Rolls brakes are an expensive nightmare to maintain. You need to find an independent mechanic that knows their way around them. Also join all the Rolls forums you can find. Good luck!
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40-something years ago, as an apprentice, I was ordered to change the brake pads on a sixties Rolls. It belonged to a friend of the dealership owner.
Just thinking of this job now, make my feets wanna start running again.
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LOL… I definitely understand. It gets easier when you have the diagrams of the system and all the other info on how it functions…But certainly not before you have that info.
Its complex to put it mildly
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I looked a litlle on link I posted. It took me all of 30 seconds to get cross-eyed. I’d rather build space ship blindfolded than have anything do with that type of brakes/suspension.
And who was that bleeding fool who stated that Citroens were complicated?
I’ll happily send a few Rolls’ses his way, just to cheer him up. 
Its the high price of “exclusivity” my man… Very exclusive…it excludes most shops and “mechanics” right off the bat mostly… haha
Its almost the same with anything high line or exclusive…overly complex in the name of complexity. Nothing garden variety here, no quick runs to the local auto parts store either… lol…you can keep it man, be exclusive all you want.
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You can buy one bottle of RR hydraulic fluid for the bargain price of $200:
https://www.ebay.com/p/Castrol-Hydraulic-System-Mineral-Oil-Plus-for-Rolls-Jaguar-Bentley-Ships-Fast/506488661?iid=142872012065&chn=ps
OMG… Really? LOL… that is too funny. Speaking of funny I have actually had many instances of talking people out of “bargain” Rolls Royce purchases. The prices seemed more than reasonable and truly incited thoughts of this being a feasible idea. Personally I have even pondered it, I mean I get a pretty free pass when it comes to any mechanical actions needed, its just everything else I guess. I really didn’t know it was as bad as your example shows it to be, that is just preposterous.
I do find it funny watching people buy outside of their “ability to own properly” Rolls or other makers…it happens rather often actually. It is a sad state of affairs in reality…watching said vehicle getting downgraded or misdiagnosed and or otherwise treated to a less than perfect upkeep.
There should be a new word for this phenomenon… This could actually be a funny new term. What would this word or term be, people of Cartalk? I’m sure y’all can come up with some funny ones.
Upkeepus Insufficientes ? Sound like something you can be afflicted with…No?
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If you must ask what it costs to maintain it you can’t afford it.
if it’s not an official term it should be!
Would Cramer call it ‘dwindling liquidity?’
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James May of Top Gear did a story on that show before he became wealthy on his Bentley saloon. It was about 15 years old and had its share of problems like any older car would. He complained about the breathtaking cost of parts, but swore he’d keep the car because he loved it so much.