I made this simple program that you can use to test if vsync works correctly with your Dosbox settings. The program sets up VGA mode 13h (320x200 @ 70 Hz) and draws a horizontally moving vertical bar. With good video output without tearing, the bar should never break up into several misaligned chunks. Also, Dosbox should not slow down in fullscreen. When you quit the test by pressing any key, the program tells you the FPS, which should be close to 70.00.

The attached ZIP file contains the program and the source code. Usage: start TEARTEST.EXE in Dosbox and check that there is no tearing. Quit by pressing any key and check the FPS report.

Good video output example:

Bad video output examples with lots of tearing:

edit:
fulldouble=true eliminates tearing, but combined with auto-adjusted cycles (cycles=max or cycles=auto) results in very slow emulation due to Dosbox adjusting the cycles to a very low value. If, like me, you can't find any combination of settings that lets you use auto-cycles and still have tearing-free video, try this version of Dosbox and set vsync=true and threading=auto: VIDEO - Vertical Sync (SDL1)

edit2:
The background intentionally pulses with a dark red color. The intention is to force Dosbox to update the whole screen.