1 headlight will not shut off, battery now dead

old old old car.38 years later.

when did it last run good, last week , last yea,r last decade/?
fast idle is vacuum leak, or bad IAC. 1500rpm cold is normal not 3000
overheating has many causes. (huge) need a list or just wan to buy tools to test it and find it.> ???
gue$$ing is hard, work and a real slog. hear goes 1 slog1.
due to age here is the list (a test each)

running 38 year old antifreeze? Lol ?
38 year old thermostat? 7 years is design life EOL ,oops.

engine compression test passes? 180-PSI? wot done?
rad and engine block flushed out of red rust mud.
38 year old water pump is no good nor is the belt. now.

RaD LEAK DOWN TEST, A TOOL; PASS OR FAIL.?
RAD , gas test (exh) a tool that see exhaust fumes in the RAD coolant, green/blue tester all shops have all this here. I typed.

water leaks anywhere under car or passenger toes. , not the side tank blow out you told and is clear
see milk-chocolate for oil in pan, oops leaks. coolant.
see milk-chocolate in tranny pan (did sticked , oops)
Rad CAP must be replaced this old. the rubber gasket in it is dead.
next is see oil or carbon dust in the RAD neck cap off dead cold engine. and full to the top of said neck. (free test eyeballs)

ok all is good above and does it overheat only parked or driven or both or only AC on. or all the above, I bet yes all.
if overheats parked, the fans must all be good are they.?

If still overheats we use IR gun tool and run the beam ever every inch of RAD TUBES. and must show 50f degree variance or more
per tube end to end if not that TUBE is clogged up, RAD BAD./
that is all for now I can do more. if need be..

on simple cause is not checking RAD water level dead cold engine
and making sure that side spill tanks has good tubes inside and work (as engine cools it sucks back coolant.) if tubes bad fix them
or check coolant like 1929 days,RAD cap off. look cold.
Coolant expands naturally hot. that side tank captures it for next cool down cycle and bad rad caps to wreck this cycle.
full stop fingers tired.

pretend caddy here,,, funny then and Diane Keaton hot .(x100)

the bug only needs a fan belt to stay cool.... (owned 2, 1970 to now)

https://youtu.be/Xo2kSu6O8cU?t=2

keep cool.
the side tank blow outs are also warped heads and or bad headgasets
if you see STEAM at tail pipe end hot engine the head gaskets are bad. 1 or both. or far worse crack block.or cracked heads.
id have looked at the tail first. (steam in front yes, look in rear)

What make , model an year vehicle ? Does the vehicle over heat ? Check engine light on ? Clogged heater core ? Did you have a cooling system flush done.

bad hoses.!! heck they are 10 years old, none last for ever.
a hose that fails is a bad hose. but some old hoses can be
pushed of the edge, sure, but hose is bad never the less.
is the rad cap new,? (do that first) use correct cap, pressure rating
never over 14psi.
my guess is you have venting? (name all overheating facts, SIGNS)
arethere signs oif steam and oil and carbon in the rad side tank or at filler hole (cold checked only)
if yes, that can be bad head gasket or far worse.
get the rad pressure checked (hand pump) leak down test.
then check the rad for exhaust gasses. blue/green tester.

does it only overheat parked.? when?
if it stays cool moving that means the fan is dead, parked.
the natural pressure is 12-14psi regulated by the cap.

you need to do tests first. not change parts.
are you going to replace all parts only to find a warped head.?
i cant hear engine run, nor do rational analysis.
nor see it mess up, or when and how bad. not me. im blind.
asking net bunny's (blind) how to fix this is over the top.
why not get the car serviced by a pro that has all those tools.
(at least 3 tools)
compression tester.
rad leak down finds leaks and if block head cracked or head gasket blown.
green/blue rad cap tester. (exhaust leaks)
a pryo IR heat gun to measure for hot points. (checks cores easy)

Yes, that should be fine, especially if you have drained the system. Fill your rad, wait to see if it goes down on it's own then top up. Turn heater on full and start the car with the rad cap off. Keep adding until coolant isn't going down. Once the engine comes up to operating temperature, replace rad cap. Then shut down car and let it cool down. Then once it has cooled down, top up coolant reservoir to full mark.

Make sure rad cap is back on the rad before shutting down the car as it will overflow hot coolant all over if not...

full flush it yet. (AF change out is very limited)
rad tubes clogged, use pyro gun to find this easy.
bad pump. all AF goes acid if IGNORED.
fan belt slips.
Rad fans dead.
thermostat upside down
thermostat bleed hole not up hill , trapping air in block making gauge fail too.
is the block really full of AF or are you reading the liar tank, onside.
check rad levels in the RAD cap neck for full or not. dead cold.

is it is really overheating or only the fibbing gauge , tells you that,?
no steam?
no bursting of AF out side tank
no pinging,?
no loss of power.?
lots and lots of signs , not one stated.......do so please.
A/C trips off line? (it too has over heat detection)

can be caused by many things.
does it leak (overheat) all the time.
does it do it at first start, parked, idling, for 5mi, or 30min.?
or only after engine warmup ,then i drive and only at stop signs
does it overheat moving fast , steady 45mph speed?
there are many tests, all are easy.
first off , it can be bad RAD,thermostat, lost coolant (ignored service) bad water pump, bad RAD CAP.(replace if bad)
or cracked engine bock, cracked head, bad head to block gasket.
to name a few.
if it only fails at stops signs look for RAD tube blockage
i use an IR pyro gun to find these.
there are 3 more tests, ask.

would bleed the heater rad .the smell of anti freeze could be from the hose bursting and going on engine

Duplicate question

you may have antifreeze in your electrics, in some cases it can turn acidic. and cause electrical faults, if you have a leak and it goes everywhere you need to flush the hole area with water to clean it off, it can even remove paint is some cases depending on the type you have put in the water system. all your wiring will need to be check and cleaned, remove battery when doing this. as you dont want to short out the battery with water.

there are oil galleries in the had so that the valves and cam can get some lubricant so it maybe that in one of those oil galleries has a crack and same with the head gasket so it could be either one