I wore a tie for my stage 2 assessments, just before We started the reactions test, the lady said we should 'make ourselves comfortable' to do the tests, including taking off our suit jackets. My advice is to wear the tie and maybe ask if they mind you taking it off just before you start the test. You can always put it straight back on after.
TDK, The interviewers certainly do travel on the trains. I found myself sat next to the chap that had just given me the managers interview on the way home. I was just about to rip off my tie, unbutton my shirt and throw my jacket over some poor unsuspecting chap in front of me when the manager sat down and asked if I minded if he joined me. I thought 'this is awkward' but was careful not to mention the interview in case he thought I was touting for answers. We generally chatted about life and circumstances and as he stepped off the train he said 'see you April 8th and good luck!" with a wink. I nearly wet myself there and then!!