Your pattern “subject + wishes/wish + past perfect” appears to be the same as my example “He wishes/wished (that) he had taken the exam”.
“He wishes (that) …” – present tense
“He wished (that) …” – past tense
“I wish (that) …” – present tense
“I wished (that) …” – past tense
etc.
There is nothing special or unusual about this; it is the same as any other regular verb.