ShellCheck does not detect error? How to fix my snippet?

I likely have syntax errors in the following (POSIX) shell snippet:

#!/bin/sh
if tput setaf >/dev/null 2>&1; then tput_init_linux else tput_init_none;
elif tput AF  >/dev/null 2>&1; then tput_init_bsd   else tput_init_none;
else tput_init_none; fi

ShellCheck 0.10.0 does say nothing about it, I found it basically by accident. I tested as follows: 1)

if tput setaf >/dev/null 2>&1; then tput_init_linux else tput_init_none; fi

this went ok: tput_init_linux: command not found 2) Reverting the logic with !:

if ! tput setaf >/dev/null 2>&1; then tput_init_linux else tput_init_none; fi

**says nothing**, but if I add one semicolon: 3)

if ! tput setaf >/dev/null 2>&1; then tput_init_linux; else tput_init_none; fi

it appears to work as expected: tput_init_none: command not found *** But I seem to be unable to chain these multiple if-statements afterward. *** So as you can see, I reached a state, where one statement works, but chaining it seems _problematic_. Can anyone help?