I'm almost positive that a brake bleed buddy won't work to bleed the clutch, unless you have a vacuum pump included with the kit.
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I'm pretty sure that if you just have a drain bottle like this,.. you are supposed to open the bleeder screw before you pump the pedal...
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Try to find someone to help you bleed your clutch.
Offer them a beer or a Big Mac or something.
Their job is easy.
Pump the pedal 3 times, then push it and hold it in.
Then you loosen the bleeder screw and drain it into the bottle while checking for bubbles.
It should only take about 10 minutes.
Don't worry about the click for now.
It could just be bubbles popping or something.
Keep in mind that the clutch master cylinders and slave cylinders on our car have been known to fail.
They are 20 years old now.
The seals on the plungers fail,..
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The bore in the cylinders get corroded, pitted and scratched and can't hold pressure.
To test for that, you can push your clutch to the floor and hold it, (once you get your clutch properly bled) and see if the pedal slowly loses pressure.
Or if you can't get any pressure on the clutch pedal at all, then your seals and bores have failed.
If your clutch pedal was working before you changed your clutch, then chances are that it is still working.