「所」 means a physical place and also takes on metaphorical meanings
ex: 「分かる所があったが分からない所もありました。」 literally means “There were understood places and also not understood places.” but could also be understood as “There were understood concepts, but also some places that I didn’t quite understand.”
「所」 can also be used with all three verb tenses to discuss places in time
ex: 「昼ご飯を食べる所だ。」 means “I’m just about to eat lunch.”
the core of the sentence is 「０が所だ。」 (“It is the place.”)
「０が昼ごはんを食べる」 (“I will eat lunch”) is modifying 「所」
ex: 「昼ご飯を食べている所だ。」 means “I am eating lunch right now.”
ex: 「昼ご飯を食べた所だ。」 means “I just ate lunch.”
「ばかり」 can replace 「所」 without changing the meaning of the sentence
as with many common expressions, the ending 「だ」 can be left off