I have go my TM back together after replacing the head gasket and need to fine tune things. When it first starts it uns like a pig until the choke comes off which is problematic. I want to try and get things a bit smoother with some carby tuning, but is there any order of precedence for carby adjustments?

Tools

I don't know whether there's any preferred sequence but I'd sort out the automatic choke first. If that's out of whack, you won't be able to judge the effect of any other adjustments. If your Gregory's manual is the same as mine, the choke adjustment is covered on page 85. Then adjust the idle speed (page 28). You're not supposed to mess with the mixture screw. If it is not running well at that stage, post the symptoms.

I took it for a 10k drive this morning and it seemed to be running ok when warm. It starts easily and is smooth but after a few seconds it gets very rough, until it warms up then it is smooth again, although idling at around 1250.In think it has something to do with the choke as if I hold it open even when cold it is smooth. I am waiting on a new tacho which should come in the mail today so will play with the choke and idle speed when it gets here. I have also had a long running issue of the tacho being erratic after the motor warms up. That seems to be not as bad now but still jumps a bit. Any ideas what causes that?
Tools

If your replacement tacho does the same thing check the connections on your coil as the tacho gets its feed from there.
1250 rpm at cold start is about the norm for the 2.6. You can adjust if if you want the manual gives the procedure its all linked to the choke and adjusting that.
Idle mixture screw is sealed from the factory.....the very first TM's may not be though. So not alot can be adjusted on these carbies in view of tuning unless you go drastic and start changing jets etc inside it. The main thing is to make sure no vacuum leaks and fuel leaks etc. V1

I agree with everything Vee said. The tachos are very sensitive and the slightest thing will make them erratic. Mine used to stop working in wet weather and still jumps and flickers intermittently.

Sorry guys, what I meant is that I have a new multimeter coming with a tacho function. Given that the one in the dash is so erratic I can't rely on that for any tuning. it will be interesting to see if the RPM will be erratic on the test tacho. Damn thing didn't turn up today though like it was supposed to and I wanted to have a go and fine tuning over the weekend. I might have a go anyway with the inbuilt tacho and check it when the multimeter arrives.
Tools

I did play around with the connections to the coil this afternoon. They looked clean but I gave them a rub with some sandpaper anyway and a spray with RP7 but nothing has changed. I don't think I have ever changed the coil since I bought the car in 1989 so I wonder if there is an issue with the coil?

Tools

hop out in the dark look for arcing when motor running

have a helper and crank while holding the coil lead to earth
see the colour and strength of spark

Tools,
I had a jumpy tacho, and in the end the coil went completely open circuit. My guess is the design of the coil terminations is suspect and this is a not uncommon fault.
The auto choke needs a LOT of TLC. The adjustment procedure is straightforward but the green cog can be easy to get wrong and the presetting of the choke lever is important to get right. There is also a 'final fine adjustment' at the top of the 'choke set lever'. this is called the 'pinion plate'. Slacken the screw and move the lever 'up' to open the choke flap more. Make sure all the scribe marks line up.
I have a mechanical tacho which I use against the cam above the water pump. Your multi meter with tacho function should be ok. I also have an oscilloscope and can do heaps with that.
The pulse waveform at the coil terminal is nominally 12 volt and this falls to zero for 5 millisec and then rises to 6 volt for another 8 msec and then the switching starts and the voltage rises to about 70 or 80 volts and of-course is a damped oscillation decaying back to 12 volt. I say all this because there may be a need to put a capacitor in the + lead to the multimeter/tacho. It's possible you may get some funny results so just read the fine print in the user manual. If u have trouble lets know.
rumpfy