The word is a noun, but we sometimes use a verb form of it instead. It is unusual because even if the word looks like a verb, it functions as an adverb, "at around midnight".
Hátinggabihín - hinátinggabí, hinahátinggabí, hahatinggabihín - This may look like an object-focused verb, but it does not behave that way when used.
"Baka HÁTINGGABÍ na makauwì si James mamaya." = Maybe it would already be MIDNIGHT when James gets home later.
"Baka HÁTINGGABIHÍN na ng uwi si James mamaya". = Maybe James will get home later AT AROUND MIDNIGHT already.
"Bakit HÁTINGGABÍ ka madalas dumaratíng ng bahay?" = Why do you often arrive home at MIDNIGHT?
"Bakit HINÁHATINGGABÍ ka madalas kapag dumaratíng ng bahay?" = Why is it often AT AROUND MIDNIGHT when you arrive home?
When "hátinggabí" is used, the time is given more focus, while when "hátinggabihín" is used, the verb that occurs at around midnight is the focus.
"Hátinggabí" is also the title of a well-known Filipino "classical" piece of music for violin and piano. In case you're interested to listen to it: [url=https://www.youtube.com/watch?v=kPQRGanwmE8]https://www.youtube.com/watch?v=kPQRGanwmE8[/url] .