I'm a lifelong artist and owner of a museum display with many thousands of miniatures. I'm going to share the method I would use.
I'd probably use acrylic for this job, it's quicker drying and easier to use.
First, Google 'mahogany wood bases' and screenshot this to refer to. Have it by you when painting.
Look at how the bases have a black line around the top or bottom or both. Observe the colours you can see in the light, medium, and dark areas.
Mahogany has a lot of red in it; to paint something like this I would prepare a palette of scarlet red, maybe crimson red, black, bright yellow, sienna brown.
Paint the black line defining top and or bottom of the base, first. Don't fuss - it will be softened by later overpainting. Just paint it.
Using thin bright red paint, wash over the rest of the object following 'the grain' of the wood. Let your brush strokes suggest wood grain. Let dry or nearly dry.
Tip: Use a tissue while painting to take some of the wetness from the brush. You want thin flowy paint, but lessen the wetness by touching brush tip with a tissue while painting. Take off too much paint on the object, with the tissue as well.
Having painted the object red, which will help your piece have the back-glow that mahogany does, lightly overpaint with a browny orange red. Blot as needed with tissue. Brush strokes should follow the grain - go around around base, or across a square one.
Let dry or almost dry, then paint the somewhat higher areas where the light hits the surface of the base on the top, at one side, a browny orange-red colour (mix scarlet, yellow, and a tiny bit of black).
While that is still wet, add a little white to that colour and put that on the very lightest areas.
Let it dry, then overpaint lightly with any of the colours to get the desired effect.
Stop before finished - don't labour it - to keep the work fresh.