Recruits

To recruit to the Eyrie or to Jack Havig's rival group, it is necessary to find people who are already time travellers whatever their other personal characteristics.

To recruit to the Time Patrol, it is necessary to find people who will accept or preferably welcome time travel and whom it will be possible to train for Patrol work.

Wardens and Rangers do not recruit with the single exception that Storm recruits Malcolm Lockridge to help her in an emergency.

Other time travellers do not recruit.

My theory of why Wells' Time Traveller did not return is that he was recruited by future time travellers.

See: 

Whatever Happened To The Time Traveller?