A slower walk can give a conversation time to become more personal.

Pace sets the depth of what gets said. Hurrying somewhere keeps talk near the surface, because the important things need a run-up: a silence, a change of subject, a moment where nobody has to look directly at anyone. Walking side by side supplies all of that, and the absence of eye contact makes honesty easier rather than harder. Nothing has to be arranged; the time itself does most of it.

When you next need to talk to someone properly, suggest a walk and take the longer route. Leave the pauses alone. What matters usually arrives near the end, so do not turn back too early.