Hi,
To back up what Dave said, the Opus ignition unit was always prone to failure, originally associated with high under bonnet temperatures but later with age, corrosion, water damage and the like.
There are various options if if goes wrong, ranging from a replacement s/h unit through replacement units which are visually indistinguishable from the original, to complete replacement using a replacement which does not pretend to be the original. I know little about the last option, other than that a Crane ignition unit is quite popular in Australia and may be available elsewhere.
S/h units are likely to be as unreliable as your original so a new unit is often the best course. Until recently there were two options, the SNG unit, still available as an exchange for your original and using a design from the later XJS version of the system, or alternatively, the ReOpus unit from Dave Curry in New Zealand. Dave recently went into semi-retirement so no longer supplies complete units, though he still supports previously supplied units. However, his excellent website is still available at:
http://www.reopusignition.com/
This site is a must for any V12 Jaguar owner with the Opus system (which includes all Series III E-types). It may help you to diagnose the fault.
The SNG unit has good reputation and is a good option, but as others have said, there are other things to check first, including the distributor cap, rotor arm, air gap (between sensor and magnetic impulse disc), leads, plugs, and connections.
Good luck diagnosing the problem.
Regards,