Eggs? OMG, spiders lay them by the tens of thousands, generally up in your headlight is the most common sheltered spot for spider egg laying. They wait for a thunderstorm and then they hatch out and play themselves down little bitty spider silk threads when the wind is up, so as to get dispersed as far as possible when the little thread snaps and the wind carries them away.
Problem is your Savage sounds a lot like a thunderstorm when it is running, and the wind is there so the little buggers thread themselves out all over chest and down your collar and up your face plate before you even get a good idea about what is happening.
"Little new-born spider, flew up the rider's snout,
Down came the sneeze and flushed the spider out.
Out came the sun and dried up all the sneeze,
Little bitty spider was up again, quick as you could please.
Up rolled the eyes and the shouts of pain began,
Little bitty spider, he had a poison gland.
In the mortuary, the mortician began the cut,
Slice went the knife and the spiders came pouring out.
The mortician he went crazy and he began to run,
Little bitty spiders, they climbed up and found his bum.
So the moral of this story is
to keep your headlight sprayed,
Them little bitty spiders, they are not fond of Raid."
The End