Sure enough, the clutch master cylinder (thanks, Og!) is empty and close examination reveals the slave cylinder has become...incontinent. Ew. Sneezed the stuff right out.
Rather a lot of rust on the slave, the cute little banjo bolt where the hydraulic line connects to it and, presumably, the not-viewable mounting bolts as well. Given that the line itself is all of maybe 3/16" OD, I will only try to do this myself if the towing fee is outrageous, as I can see it turning all too easily into an end-to-end replacement of the entire system. Fiddling the new line into place, unhooking the master cylinder linkage from the pedal arm and bleeding the darned thing each look to be exquisitely fiddly and/or awkward tasks. An MGB, this car is not; I've done this exact job on one (or maybe two -- people will put DOT 3 fluid in them and it eats up the seals)* of those and it was fairly straightforward.
* If you buy an MGB from someone's front yard (garage, whatever), you can just about count on having to rebuild or replace all or part of the clutch and brake hydraulics. It is at that point that you will appreciate the wide-open, lawnmower-simple layout of the mechanicals: except for a fiddly clearance in removing the clutch master cylinder (not a problem in the right-hand-drive version), none of it is difficult to get to or hard to figure out.
Introduction to Sim
5 months ago