timekeeping, merge & sort non-adjacent cells

bringing this back without the original posts, as this one sums it up best.
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Typically there are 4 rows for each person with two Times on each...a login and logout.
They login in the morning, logout for break, log back in, then out for lunch, back in after, logout for break #2, back in, then logout for the day.
Getting those 4 rows of two each to a single row of 8 is the object.
I'll attach copies of the actual worksheets, but basically they are:
......A........B........C.........D....
Date - Login - Date - Logout is the starting format.
2
3
4
5

What this person is currently doing is manually cutting and pasting
B2
D2
B3
D3
B4
D4
B5
D5

to get the times into one column in chronological order. my hope was there would be a way to have that step automated. If an individual has fewer than 8 times for a given day, they just paste as needed rather than all 8 at once.

if it can do more, that's great, but just getting those 4 rows of 2 to a single row of 8 would be a big help.
Thank you!

One thing I thought of, but don't know how to execute, is to search based on the unique identifier, the person. There will be multiple matches if a person has 8 total times. Of those multiple matches, specify a cell to return the 1st match of column B, the next cell would be the first match from column D, then the 2nd match from column B, second match from D, etc. Am I on the right track?