To use brifters, there are two issues.

First, road handlebars are usually 23.8 mm diameter while upright/mtb bars are 22.2 mm. Some brifter levers will tighten up adequately on the thinner bar, others won't. Most mustache bars are 23.8 mm .

Second, the handlebar has to have a pretty tight curve so the brake lever will actuate. This rules out any straight bar and most other upright bars.

Most "mustache" bars can be made to work, especially with the older Shimano brifters. Campy Ergo levers, with the thumb control, are more difficult.

Getting a mustache bar set up so your neck is happy, this isn't something I can speculate about. I've done it successfully once, and failed miserably more than once.

Good luck!