First, a Solar Eclipse is a localized thing. Only a very tiny portion of the surface of Earth ever sees any particular solar eclipse as total. In order to change that, you would need to make the "moon" considerably bigger than that "planet". This is what happens in a Lunar Eclipse (The Earth eclipses the Sun relative to the Moon, and its shadow covers the whole moon)
solarEclipse.png
lunarEclipse.png
Second, to be "stationary" like that, you have to put the moon at the L1 point, or really, given how big the "moon" would have to be, you'd put the planet at the L2 point. Neither L1 nor L2 is stable in the long run though.
The only way I see that you could maybe make this work would be to put your planet at the L2 point of a gas giant, where it would be knocked loose rather readily by the influence of other planets or the giant's normal moons. If it somehow stayed in the L2 position, it would be frozen solid and completely uninhabitable.
So just call it magic. Go with a planetocentric model where the sun is small and goes around the planet.