I, too, would suggest the relay, but, looking at the Bentley
manual reveals there is no headlight relay on an '83.

The ignition switch is also probably not the problem and you
can verify this by noting whether, for example, the
taillights remain lit, and if they are this would mean that
the headlight switch itself is also stuck in the "on"
position because it's between the ignition and the
headlights.  This seems pretty unlikely given that it's a
rocker-type switch and you could probably feel if it's
broken.

The actual culprit is probably the turn
signal/flasher/high-low switch itself, which has an
independent source of always hot (unswitched) current.
(This permits flashing the high beams as a warning whether
or not the headlights--or even the ignition--are switched
on.)  I suggest this switch is stuck in "flash" mode.