Can anyone point me to the cause of an electrical drain?

Hi all,
I'll preface this by saying that I am an amateur. I recently decided to try and get
my Grandma's '86 Nissan 300ZX (Z31) automatic naturally aspirated V6 (non-
turbo) two-seater running. It has sat in my Mom's backyard without being
started for at least 10 years. If I boost it, or if the battery is recharged using a
trickle charger, I can normally start it for between 30 seconds and a few
minutes at which point it dies, and the battery is drained to zero. Sometimes
the dash lights come on, sometimes they don't. Based on everything I'd read
online it seemed that the alternator was the culprit, so I replaced the battery
and the alternator (with a rebuilt unit from NAPA). This made no difference. The
car still starts only when the battery is fully charged or boosted and soon shuts
off. I haven't even successfully shifted the car into drive. To me, it still seems
that the problem is electrical, but I don't know where to look next. Any nudges
in the right direction would be really appreciated!

Thanks