Driver's side in the UK/Japan/Australia, so it's easier to hear. At first it sounds like an HLA or a stone caught in the tyre tread, but it doesn't vary with road speed or engine rpm. Far more noticeable with the top down.
Only does it when the car is under power and on a light throttle (say
30mph in 4th or 40mph in 5th).It can't be replicated when the engine is idling.
Anyway, it turned out to be the purge valve, which is the little thing with two vapour hoses and an electrical connector bolted directly over the RH front suspension turret. Only 5 minutes' work with a 10mm wrench to fit a new one, but the part costs at least 48UKP over here, twice that if you go into a Mazda dealer!
I don't know the possible consequences of leaving it unfixed; but its function is to allow the inlet vacuum to suck the carbon canister of fumes under conditions when the engine can tolerate a bit of extra fuel in the mixture. The ticking is probably a stuck valve, and the solenoid frantically trying to open it. On a US car you *might* get an emissions warning light; UK cars don't have one, although all the emissions control gubbins is the same.
Might help someone; it's a common problem on the UK MX-5 owners' club forum :-)