I ride a 2003 Heritage Softtail Harley Davidson that I bought used about a year ago. When I turn the ignition on, the system lights come on and the oil light stays on but goes off when I start it. Is this normal or am I just paranoid?

Yes that is normal. It's a way to test your lights to make sure they are working.

When you turn key on, it puts power to one side of the indicator, the ground is gotten through the Normally closed oil pressure switch, When it is started, Oil pressure opens the switch. If you DON't see the light when first turned on, check bulb.