I think both of these questions should be tagged time-constant.
time seems to be useful for some of its questions, such as those which involve determining system time, measuring a time, or perhaps to refer to time domain as opposed to frequency domain. On the other hand, there are questions about settling and charging time for which it may not be appropriate, and there are questions which should instead be tagged with the existing and more specific lifetime (e.g. this one about battery lifetime).
constant doesn't seem to be particularly useful for any of its questions. It is mostly used in questions about constant voltage, constant current, constant power, etc. There is already a constant-current tag, and in any case voltage-source, current-source or constant-current, and power-supply seem to be better tags for these questions.
What should be done with time and constant? Should they be removed entirely? Should we simply clean up those questions tagged with them that can be re-tagged with more specific tags? Should we not bother?