After 8 years the fuel is bad, most of the octane has gone. Fuel injectors need cleaning, and anywhere the fuel has touched, especially the Throttle Body and MAF.
Parasitic draw on a battery is hard to diagnose. I wrote this Tip.
https://www.fixya.com/cars/r29903527-parasitic_draw_car_batteries
You need an auto electrician, a pro grade scan tool computer can diagnose in 20 minutes, for the starting issue and probably another hour for the drain.
https://www.google.ca/search?q=mobile+auto+electrician+near+me
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I drove one in 1974 my friend, I had TR4, Triumph then.(just back from NAM)
ours with both stick shift never seen an automatic then.
who made that Hydramatic then?
cranking the crank shaft seen is spinning? fast.?
check compression?
seems to me it blew up the starters over-running clutch rendering the starter useless, really look at the crankshaft pulley first;
if crank is dead, and starter motor SINGS high, the clutch on the starter pinion shaft was wrecked,
if it is a flat belt--probably not
google-- vintage and antique car clubs --- and ask around as there are owners of the make that will know where to get a belt or who can make one
Having some experience of those old engines I would have guessed 0.012" but the forum says 0.015" which in the old days was used on factory stage 1 tuned engines. Using 15 thou with a standard engine increased valve noise a bit but did give a slight increase in mid-range power.
It is wise to trim the feeler gauge to slightly less width than the valve stem diameter in case the rocker arm faces are worn.
Austin and related makes/models, unlike other brands, specified static valve clearance checking and adjustment though dynamic checking could be used if preferred.
http://www.automobile-catalog.com/auta_details1.php
http://www.oldclassiccar.co.uk/forum/phpbb/phpBB2/viewtopic.php?t=18232