I'm going to concur with sec101 on this. If your switch ports are not set to go straight into the forwarding state, you may have delays while STP goes through it's learning process. 15s sounds about right. If you are using Cisco equipment, that's the default learning timer. I'm not sure how this is affected by Passive Link State: auto, but you should probably have these ports in "portfast" mode (Cisco speak) or "edge" mode (Juniper speak) either way.
https://www.cisco.com/c/en/us/support/docs/lan-switching/spanning-tree-protocol/19120-122.html
forward delay—The forward delay is the time that is spent in the listening and learning state. This time is equal to 15 sec by default, but you can tune the time to be between 4 and 30 sec.
PS - Also agree with using "suspend" instead of just reboot for HA failover. Upgrade the Passive node first thus reducing your failover to a single event as well.
