How long might a tick be on a body before biting?
They wander the body for 30 minutes to an hour before inserting their feeding parts into the skin. Source.
It entirely depends what material you are wearing, i.e. fluffy wool is difficult for them to climb on. They can fall off somewhere in the home and bite another day.
2mm nymphs climb on human skin at about 10cm per minute, so it could find the back of the knee in about 5 minutes and search for a bite site. tick attachment site distribution is: 9% head-neck, 5% arm,
24% stomach-groin, 7% back, 18% chest-shoulder, 25% leg-foot, and 12% hip.