I have had many odd encounters with spiders in my lifetime. The oddest however was in my car. I watched a spider of the small jumping kind crawl up from the floor board, across the dash and onto my steering wheel column. It then climbed out to the end of the steering wheel column, closest to me, and stood there. It seemed to wave a couple of its front legs at me. Being very Arachnophobic myself all I wanted was to get it out of the open window. I raised a book up to the steering wheel and the spider hopped onto it. I then went to shake the book out the window but panicked and dropped it into the floor board instead, along with the spider. I stomped my feet Hoping to either step on the spider or Scare it away. What happened instead really shocked me! I watched the spider come crawling up out of the floorboard, back across my dashboard and back out onto my steering wheel column in front of me once again. The exact same place it had been before. It once again sat there calmly staring at me. Intrigued but still frightened I once again put my book up to the steering wheel and the spider hopped onto it, and this time I more carefully shook the book out the window, causing the spider to fall outside. Now I ask you, does this seem like common behavior for a spider?
Hopefully, none of these events transpired while you and the spider were driving!. It would be fun to say that you had a friend in the making, but perhaps that is a stretch. It does seem like you had an encounter with a jumping spider.
Jumping spiders are active hunters with well-developed eyesight; they use their vision to study and track their prey. These characteristics make them appear to have a great deal of curiosity and personality. At least a lot more than their web-building brethren that just sit and wait for some unfortunate passerby to fly into their web.
All human comparisons aside, jumping spider display a good degree of site fidelity, meaning they will stay in a “good” area (where they have prey and constructed nest, etc.) and attempt to return to it if displaced.
Also, because of their use of vision in attempting to determine if something is suitable prey, they will stare and turn to follow items. Perhaps there was something on the steering wheel or you that caught the spider’s attention. Their visual field extends about foot, so that can be a gauge for determining what may have caught its attention.
Jumping spiders often wave their pedipalps – leg like structures at the front of their head – which is probably what you observed waving. They use these to signal other members of their species (mate attraction) and to help capture prey. They do not just rely on vision; the pedipalps also contain sensory organs, so they move these around to contact substances and sense what they are. (Watch an entertaining video of a jumping spider.)
So why did this one spider appear to be so bold? One common species across much of the US is Phidippus audax – the species name roughly translates as the “audacious” or “daring” jumping spider. Perhaps, it was just living up to its name.
In the end, a lot of what your little friend was doing are common behaviors for a jumping spider. The circumstances of it occurring in your car is perhaps a little uncommon.