Triumph Thunderbird. Poss Head Gasket Problem

Hi
Apologies i put this in wrong place originally as new to this forum and triumph motorcycles.
Just took delivery of bike sold by po as a project but mechanically solid.
Started ok first press but will only run on choke even when warm and any blip of throttle engine bogs and will stall unless quick on the choke. When running engine is smooth and no misfire at all. Figured this meant a carb jet clean so they are out and ready to dismantle.
Whilst doing this found the coolant tank empty. Difficult to see from outside but looked dry as far as I could tell inside. Worried about head gasket now but wanted a bit of advice on best way forward to test before going straight in with taking head off etc . Lots of other things on bike will need advice on but this is the major issue and only 4 days into ownership !
Any help greatly appreciated. Bw. Rob
Update- topped up rad and system took about 1.5 litres . Oil looks OK in window. Plan is to clean carbs and run up to temp gently and keep a close eye on what happens to cooling system and exhaust smoke. .any help or advice much appreciated. Bw Rob

 

Thanks all for comments. Put carbs back on bike and ran for full 10 mins. No smoke from exhaust or water leaks etc. So looks like head gasket ok.
Tickover without choke still an issue but think this just needs adjustment.
Next query is how long before fan should start if bike is ticking over. Appreciate depends on outside temp but wanted to know if fan operating correctly.
Thanks again. Rob

 

Update to last item.
Carburettors cleaned and bike runs well. May need v slight adjustment for tickover but that's all.
Anyway as noted have been running bike for 10 mins at a time and no cookant leak . I have replaced fan as was not working and have tested the circuit to it and it operates when I connect the two wires going into the thermostat housing.
But so far I don't seem to get the fan working. I am not sure if bike is hot enough for fan to start or the switch in the housing is faulty. Not helped as I know the water temp warning bulb is not working.
Does anyone know how long at tickover before fan kicks in. I am not getting any water leaks at all at radiator cap or expansion tank. Looking into radiator when running no evidence of bubbles so think head gasket is ok .
Appreciate any advice. Thanks Rob