(for) a space: for a short period of time; for a while. Cf. sense 5a. Now rare.

for a season: for an indefinite period, for some time, for a while. Similarly, for a long, short,etc. season. Also adverbially, without for.

In adverbial phrase the whilst (obsolete or archaic), also (rare) †to whilst, in the whilst, or as simple adverb whilst (obsolete exc. dialect)…

for a spell, for a time. In U.S. without preposition; also a spell ago, some time ago.