Past Wishes

Grammatically, the Past Wishes have two important elements: the WISH Clause and the THAT Clause. 

WISH Clause + THAT Clause = Past Wishes.

The WISH Clause is formed by: A Noun and wish.

A Noun + wish = WISH Clause

The THAT Clause is formed by: That, a Noun and a sentence in Past Perfect or Could have and Past Participle.

NOTE: the word "that" is often omitted, because it is implied in the general sentence.  

(That) + A Noun + Past Perfect = THAT Clause.
(That) + A Noun + Could have + Past Participle = THAT Clause.