What would cause the park brake light on 2002 neon dash to light up when starting from stop especially on up hill grade?

You need to ad brake fluid. The sensor senses there is less fluid when it all gets sloshed around (like your gas gauge). That should fix the prob. my 95 neon had the same problem, parking break light and exclamation symbol light. the break fluid sensor is hooked up to these lights, filled up the break fluid and problem went away, but came back a month later.. searched and found a leak in the break lines and fixed it.