Welcome to FT posting!
In these situations I usually check bags. Baggage can be loaded onto your departing flight even after the boarding door is closed - they have a much better chance at making a short connection than you do if you have to wait for pink tags.
All things that can (and have) impacted pink tag delivery:
- elevator is broken
- too many bags for the cart so they need two (and your bag will be on the second cart)
- confusion by gate and ground staff as to where the bags will appear