oooo how exciting, your little one will be here soon!

I'm not sure my first S&S did anything to be honest, I had the same 'stats' as you and made it to my 41wk aapointment! the pink bleeding is normal as your cervix has been aggravated

My second S&S however, 4 hours later and I was in 'noticeable' labour- i say 'noticeable' as I'd been having contractions for a week.... but they definitely amped up a notch!!! I remember losing my plug before everything started though, so that might be your next sign.

Best of luck, look forward to seeing your BA soon!