Bright light at car level

I was driving down the cane road going home at 8pm When a really bright light came behind me.  I drove for a distance then tried to wave the vehicle to pass me.  The light was at car level, so I didn't think much about it.  I tried to wave it over again, but it wouldn't pass.  I slowed down.It slowed down.  I sped up. It sped up. Keeping my exact speed.  I backed up, it backed up. Finally I pulled over to the side of the road to let it pass,cane roads are very narrow, one lane.  It stoppped. I shut off the engine, there was no sound coming from its engine.  I got out of my car but the light was so intense that I couldn't see what was there.  I started to walk towards the light.  I stopped about 10 feet from it.  I still could not see or hear any vehicle.  Only silence.  I thought it wasn't wise to persue this any further, so I walked back to my car and got in.  Now this was a matter of a few minutes.  As soon as I started to drive away the light disappeared. When I got home, a 15 minute drive, my roommate asked me where I'd been.  I told him I came straight home.  Why?  Then He told me it was 10pm.
I told him what I had seen.  He didn't want to talk about it.
Has anyone else seen this.
I didn't go anywhere but to see this and straight back to my car.
I know it has been some time since I've seen this, but I didn't know about these sites.
Date is approximate.  PD