Vesafb is a framebuffer driver for Intel architecture that works with VESA 2.0 compliant graphic cards. It is closely related to the framebuffer device drivers in the kernel.
vesafb is a display driver that enables the use of graphical modes on your Intel platform for bitmapped text consoles. It can also display a logo, which is probably the main reason why you'd want to use vesafb :o)
Unfortunately, you can not use vesafb successfully with VESA 1.2 cards. This is because these 1.2 cards do not use framebuffering. It may be that someone will write a vesafb12 device driver for these cards, but this will use up precious kernel memory. :o(
There is however a potential workaround to add VESA 2.0 extensions for your legacy VESA 1.2 card. You may be able to download a TSR type program that will run from DOS, and used in cojunction with loadlin, can help configure the card for the appropriate graphic console modes. Note that this will not always work, as an example some Cirrus Logic cards such as the VLB 54xx series are mapped to a range of memory addresses (for example, within the 15MB-16MB range) for frame buffering which preludes these from being used successfully with systems that have more than 32MB of memory. [There is a way to make this work, i.e. if you have a BIOS option to leave a memory hole at 15MB-16MB range, it might work, but I've been told that Linux doesn't support this] If you wish to experiment with this option, there are plenty of TSR style programs available, a prime example is UNIVBE, which can be found on the Internet.