Track all of one dir but only specific files in another

Question

I have a fresh git init --shared which results in:

.git
/dir1
/dir2
.gitignore

I want to track everything inside of dir1 and only .conf files inside of dir2.

So far I have this in my gitignore but it's not working as expected; dir2 remains totally untracked.

# Track the root
!/

# Omit every item under the root
/*

# Track dir1 under the root
!/dir1/

# Track .conf files anywhere
!*.conf

# Track .gitignore under the root
!.gitignore

Output of git status:

.gitignore
dir1/