Hi , The Chinese MG TF's had a Thatcham 1 alarm system with a sealed alarm and battery backup under the bonnet. RHS , hidden behind the ABS pump mounting shelf. If this is what is ticking It may be this is your alarm/immobiliser issue.
There is a SCU (security control unit) behind the centre consul to the rear of heater controls. This is a Pektron unit that has known issues with dodgy relays. If the ticking is coming from there you may have a faulty SCU. If so look up "Technozen" who is the expert at fixing them.
If the ticking is coming from your right knee when sitting in the drivers seat of from the LHS under bonnet you may have a relay problem in one of the fuse boxes.
If the ticking is over your left shoulder when in driving seat, that's the fuel pump. Those are all the ticking things I can think of to look at
The P0001 code may be coming up if the immobiliser is not switching on the fuel pump.
Low battery voltage can also give alarm/immobiliser issues
Since this is intermittent it dose sound like bad contact/earth, or a dodgy relay.
Good luck!