alternate means 'one after the other' or 'each succeeding the other in turn, especially continuously' and alternative means 'one instead of the other' or 'allowing or necessitating a choice between two or more things'
be remembered, be repeated, come again, come and go, come back, crop up again, haunt thoughts,
persist, reappear, recrudesce,
return, return to mind,
revert, run through one's mind, turn back