Might be worth cleaning the turn signal switch contacts also. I recently had some issues, a little different from yours that were cleared up with a cleaning of the contacts.
Switch Cleaned and working properly.
The problem only exists when temps become 40 degrees or colder.
the colder it becomes the longer the blinkers take to function.
Functionality.....They work after everything becomes/gets warmed up
This relay that was mentioned earlier I believe replaced will solve the issue.