The next query tries to correspond to your question:
;
with Q1 as
(
select *, case when lag(Response_) over (order by Client_Date) <> Response_ then Client_Date end as f
from MyTable
),
Q2 as
(
select *, max(f) over (order by Client_Date) as m
from Q1
)
select Endpoint_, Version_N, Response_, Endpoint_, Client_Date,
dense_rank() over (order by m) as TrackerID
from Q2
order by Client_Date
It assumes that Client_Date includes distinct time. It is necessary to have a column that can be used for ordering.