If I understand the diagram showing the Moon phases according to FE Wiki, the new Moon should always appear in the sky 'underneath' the Sun.
This is another great subject to discuss with diagrams and illustrations.
See, there are two FE ideas about Moon phases, one use a gigantic 30km in diameter obscure anti-moon object that nobody saw, the second is very similar to the real thing,
the Sun illuminating the Moon but we see in angle and only part of it illuminated. This second also eliminate the idea about the Moon has own light, being transparent, being a disc, etc.
The problem with the underlined above, is the FE distance of Sun/Moon and the observer, it is too short, less than 6000km. Suppose the Sun/Moon position is at longitude X, and two observers, one 5 hours to East, another 5 hours to West, each would see a complete different illuminated Moon covering. One would be more illuminated area, the other will see less illuminated area. The distance from Sun to Moon will not change the different view much. This only works well if the Sun/Moon would be very far away, so the angular position of the observer on Earth will be visible and angular insignificant to notice any difference.
This simple observation can be done by several people at some specific time all over the world where they can see the non full moon. The Moon on the pictures could be measured; diameter and illuminated area/angle. If there any difference as viewed from different places over the Earth, then the observes's angles could be calculated and confirming the Sun/Moon altitude over the FE.
The only way for FErs to have the same illuminated area view from different and far places, is for the Moon not to be spherical, but a flat disc facing down, parallel to Earth, but them, other large problems would arise, as; how people don't see the Moon as an elipse from an angle, and worse; how part of the Moon is not illuminated by the Sun on its phases, again, having its own light? obscure object blocking part of the disc view?
The RE heliocentric system is so easy, fool proof and works always.