On the Subject of The Glitched Button

This is a button. It is...?

The module contains a glitched button and a screen showing a cyclic sequence of 0’s and 1’s.

The displayed sequence will be found in the table below. However, one bit has been flipped.

Tap the button when the seconds digits of the timer, modulo 15, are equal to the corresponding number plus the position of the flipped bit, modulo 15.

0010111101010(contains 5 0-bits and 7 1-bits)
1001100111100(contains 6 0-bits and 6 1-bits)
2111011110000(contains 5 0-bits and 7 1-bits)
3001111101101(contains 4 0-bits and 8 1-bits)
4110101011011(contains 4 0-bits and 8 1-bits)
5010001011010(contains 7 0-bits and 5 1-bits)
6101001001000(contains 8 0-bits and 4 1-bits)
7100011000010(contains 8 0-bits and 4 1-bits)
8110010101110(contains 5 0-bits and 7 1-bits)
9010001001101(contains 7 0-bits and 5 1-bits)
10110011011111(contains 3 0-bits and 9 1-bits)
11011011000000(contains 8 0-bits and 4 1-bits)
12100010111010(contains 6 0-bits and 6 1-bits)
13100100000001(contains 9 0-bits and 3 1-bits)
14100110010011(contains 6 0-bits and 6 1-bits)