I have an old Request Tracker 3.6 setup using MariaDB 10.2.10 (recently rebuilt, was on MySQL 5.5 before and did not have this issue). I noticed that a query that includes searching by the requester Name is much slower than searching by the EmailAddress. When I look at the SQL query generated, the only difference is searching by the Users.Name column vs. the Users.EmailAddress column. The Name column is a UNIQUE KEY while the EmailAddress column is just a KEY (each of the keys has just the one column). That doesn't seem like it should cause a big difference.
I'm attaching the Users table schema as well as "explain extended" of the two queries.