Blake,

The brake light switch works on brake fluid pressure in my '84 and there
are actually two switches, one for each brake fluid circuit.  If only one
switch switches, the brake warning light comes on.  It is unlikely that
both switches have become insensitive, and you didn't mention that the
brake warning light lit.  So, the answer is without some re-design, you
can't make the brake lights come on before there is brake fluid pressure.

Maybe your worried that the brake pedal is too low ... moves too far before
the brakes start to work.  Well, that's a whole different question.

Mike  Phoenix AZ