Which encoding uses the \x (backslash x) prefix?

I'm attempting to decode text which is prefixing certain 'special characters' with \x. I've worked out the following mappings by hand:

\x28   (
\x29   )
\x3a   :

e.g. 12\x3a39\x3a03 AM

Does anyone recognise what this encoding is?

It's ASCII. All occurrences of the four characters \xST are converted to 1 character, whose ASCII code is ST (in hexadecimal), where S and T are any of 0123456789abcdefABCDEF.

The '\xAB' notation is used in C, C++, Perl, and other languages taking a cue from C, as a way of expressing hexadecimal character codes in the middle of a string.

The notation '\007' means use octal for the character code, when there are digits after the backslash.

In C99 and later, you can also use \uabcd and \U00abcdef to encode Unicode characters in hexadecimal (with 4 and 8 hex digits required; the first two hex digits in \U must be 0 to be valid, and often the third digit will be 0 too — 1 is the only other valid value).

Note that in C, octal escapes are limited to a maximum of 3 digits but hexadecimal escapes are not limited to 2 or 3 digits; the hexadecimal escape ends at the first character that's not a hexadecimal digit. In the question, the sequence is "12\x3a39\x3a03". That is a string containing 4 characters: 1, 2, \x3a39 and \x3a03. The actual value used for the 4-digit hex characters is implementation-defined. To achieve the desired result (using \x3A to represent a colon :), the code would have to use string concatenation:

"12\x3a" "39\x3a" "03"

This now contains 8 characters: 1, 2, :, 3, 9, :, 0, 3.