Sorry for continuing on the different trail but this is my favorite subject behind UConn. I almost took the cog railway once, but I had an excuse I was on my honeymoon. Likely, it was to fogged into run so all the times I've been on Washington I've done it on foot.
While the auto road is intended for, well autos, I've been up that four times. They have a running race up there and I participated in that twice. Back in the 60s I went up twice at night — the goal was to see the sunrise and we didn't want to walk up a trail at night so we figured we could walk up the auto road which worked. Unfortunately, the sunrise is visible about 60 days a year so the odds are against us and it was cloudy both times.