Write a bash script that takes two strings as arguments and performs the following string tests using if, then, else, and elif syntax:

1. Check if the first string is equal to the second string.
2. Check if the first string has a non-zero length.
3. Check if the second string has a zero length.

Example Output:

$ ./string_tests.sh Hello Hello
Strings are equal
First string has non-zero length
Second string has non-zero length

$ ./string_tests.sh Hello ""
Strings are not equal
First string has non-zero length
Second string has zero length