Although TM’s second and third (and arguably “Non-Sequiturious”) excuses are separated and prompted by your astute follow-up questions/observations, I think TM’s “contributions” to the dialogue at issue can be viewed as three basically independent alternative excuses being offered in response to your initial question, and if the dialogue had occurred in a legal setting, I’d say that TM was engaging in the generally unacceptable practice of “shotgun pleading” at worst or, at best, the similar, yet more acceptable practice of “pleading in the alternative” or “alternative pleading.”
shotgun pleading (from Wiktionary)
Noun
(law) A legal complaint or an answer to a complaint which sets forth an excessive
number of facts with no clear organization, and then asserts that
those facts describe a cause of action or a defense.
Pleading in the alternative (from The Free Dictionary by Farlex)
Noun
a pleading that alleges facts so separate that it is
difficult to determine which facts the person intends to rely on
See also, via Xmind, Black’s Law Dictionary’s definition of “shotgun pleading”:
“A pleading that encompasses a wide range of contentions, usu[ally] supported by vague factual allegations.”
And, for “alternative pleading”:
“A form of pleading whereby the pleader alleges two or more independent claims or defenses that are not necessarily consistent with each other, … .”
Although these precise legal terms don’t seem to have been widely extended to non-legal contexts, I think they would be understood outside the courtroom to describe what TM was doing.
Regardless, the somewhat similar use of “shotgun” (or “scattergun”) as an adjective does exist outside the courtroom, and although most frequently used to modify “approach,” I think it could be used here with “excuses” to describe TM’s reaction to your questions [and you could even consider mixing/combining it with the cited sense of the bracketed idiom], as follows:
“TM is just [shooting from the hip and] offering shotgun/scattergun excuses.”
Shotgun (from OxfordDictionaries.com)
ADJECTIVE
Aimed at a wide range of things; having no specific target
Scattergun/Scattershot (from *Oxford Learner’s Dictionary)
Adjective
referring to a way of doing or dealing with something by
considering many different possibilities, people, etc. in a way that
is not well organized
Shoot from the hip (from OxfordDictionaries.com)
PHRASE
informal
React without careful consideration of one's words or
actions:
‘he is shooting from the hip in an act of political
desperation’