Do I need to re-pair my Engage 55 SE when switching between two connected devices?

No. If your Jabra Engage 55 SE headset is connected to two devices simultaneously, like a Jabra Engage SE base and Jabra Link 400, press and hold the mute button on the headset for 4 seconds. There is an audible click in the headset as it toggles between the two connections.

Note
If you put the Jabra Link 400 into pairing mode, it will clear the pairing memory and re-pairing with the Jabra Link 400 will be necessary.