The question is why is the sentence A2 wrong?
A1 The man who looks/is tired is my brother. (OK)
A2 The man tired is my brother. (not OK)
B1 The man who is interested in your car will phone later. (OK)
B2 The man interested in your car will phone later. (OK)
Here is the rule:
If the relative pronoun RP is followed by a verb, the RP is the subject pronoun. SPs must always be used.
the apple which is lying on the table.
If the RP is not followed by a verb (but a noun or pronoun), the RP is an object pronoun. OPs can be dropped in defining relative clauses, which are then called Contact Clauses.
the apple (which) George put on the table.
BTW British Council Learn English grammar site describes B1/B2 as an example of a simplified relative clause. It says:
"Defining relative clauses can be simplified, or reduced, in several ways:
If the relative clause contains the verb 'be' + any of the following then it can be reduced:
(a) be + an adjective phrase
Note that other verbs are possible here as well as 'be', such as 'seem', 'look' and 'appear'.