I have seen the following occur during simulator events. With a left Source Off light illuminated and the captain's autopilot and autothrottles engaged (or re-engaged):

• Captain's flight director lateral guidance cue will bias out of view when the autopilot is disengaged PRIOR TO glideslope capture.
• Captain's flight director vertical guidance cue will bias out of view when the autopilot is disengaged AT glideslope capture.
• Flight director will bias into view when either autopilot is then engaged.
• Flight director will bias into view when either pilot selects TOGA.

I do not know why the above occurs. If anyone can explain this, I would be grateful.