Get matching pairs from text file

I have a text file test1.txt:

1   first_match
2   not_needed_line1
3   not_needed_line2
4   not_needed_line3
5   second_match
6   not_needed_line4
7   not_needed_line5
8   not_needed_line6
9   not_needed_line7
10  not_needed_line8
11  first_match
12  second_match
13  not_needed_line9
14  not_needed_line10
15  not_needed_line11
16  second_match
17  not_needed_line12
18  not_needed_line13
19  second_match
20  not_needed_line14
21  second_match
22  not_needed_line15
23  not_needed_line16
24  first_match
25  not_needed_line17
26  not_needed_line18
27  second_match

I would like to extract pairs containing "first_match" and "second_match" and add filename test1.txt before each line in result.

In this example it will be lines:

#1 and #5
#11 and #12
#24 and #27

Please note - lines #16, #19 and #21 are not included, because they are missing first matching line from pair "first_match".

I found awk (GNU Awk 3.1.6) script to extract all lines between pairs.

/first_match/{printf FILENAME " - "; f=1} f; /second_match/{f=0}

Result is:

test1.txt - 1   first_match
2   not_needed_line1
3   not_needed_line2
4   not_needed_line3
5   second_match
test1.txt - 11  first_match
12  second_match
test1.txt - 24  first_match
25  not_needed_line17
26  not_needed_line18
27  second_match

Questions:

1. How to get only pairs containing "first_match" and "second_match"?

test1.txt - 1   first_match
test1.txt - 5   second_match
test1.txt - 11  first_match
test1.txt - 12  second_match
test1.txt - 24  first_match
test1.txt - 27  second_match

2. How to get only second line from pair - "second_match"?

test1.txt - 5   second_match
test1.txt - 12  second_match
test1.txt - 27  second_match

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