Existential 'There' vs Circumstantial 'There' [Diagnostic]

Halliday & Matthiessen (2014: 309):

Phonologically there is non-salient, and the vowel is often reduced to schwa (hence identical with the); it is thus distinct from the Adjunct there which is a circumstantial element. Contrast (i) existential there’s your father on the line, with reduced there [ðə] as Subject, and response Oh, is there?, and (ii) circumstantial relational there’s your father, with salient there [ðɛə] as Adjunct, and response Oh, is he? In (ii), but not in (i), there’s is in contrast with here’s.