Thanks Martin & Joe
The stub had broken off at the carbie - knowing where to look made finding the left over hole much easier to find. I mucked around with it for a few hours this morning and after pulling the carbie 1/2 apart (until I stopped finding dust and dirt) and gave everything a good clean.
Did not have a spare spark plug so sucked on the de-compressor while rotating the cutting deck by hand. I was quite contorted; surprised GF did not take a picture!!
Anyway, contortions aside this resulted in a definite improvement in compression; so de-compressor seems to work...
Drilled out the hole where the stub was and stuffed some irrigation tube in so that I could hook up the de-compressor again (see pic). Unfortunately I managed to crack the carbie housing near the connection point - I think crack is cosmetic only, annoying.
Once reassembled the mower started 2nd pull

. Very happy considering the carbie was emptied.
However connecting / disconnecting the de-compressor did not seem to make any difference to the running of the engine, and it sounds like a tractor.
With engine running I sucked on the the de-compressor and still no change...
How does the de-compressor work? Is it:
pulsing open and closed,
or constantly closed when the engine is running?
Many thanks, S
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