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As Invisibility and Greater Invisibility are illusion spells and we know that the benefactor of the spell does not actually go anywhere else could they be seen from the Border Ethereal?
Considering See Invisibility allows sight into the Ethereal Plane is it reasonable to assume the other way is also true?
Nothing in the rules says that this is the case. Being in the border ethereal is a form of invisibility from the material plane, thus the clause in See Invisibility. Being invisible in one way does not have any effect on other forms of invisibility.
Invisibility and greater Invisibility make you unseeable to normal vision without the aid of magic or some special sense. it is an illusion spell and does not transport you or "phase you out" in any way.
The See Invisibility spell says you can see invisible objects and see into the Ethereal plane, implicitly defining them as different things, supported by other effects and spells such as Mordenkainen's Faithful Hound which also explicitly speaks about each separately. It does not state in any way that invisibility and etherealness are connected, it implies the opposite, it merely enhances the target's vision so that they can magically see both.
In addition the Etherealness spell states you see the plane you originated from, grayed out, with no mention of special senses that reveal creatures or anything else cloaked by illusion magic.
So no, someone who is on the ethereal plane has no more chance of seeing someone who is invisible than anyone else. In fact given that their vision is grayed out, it is possible that a DM may impose a situational penalty to see the clues (footprints in the dust etc.) that that there is an invisible creature present.
References:
Invisibility spell (PHB p.254)
2nd-level illusion
A creature you touch becomes invisible until the spell ends.
Invisible condition (PHB p.291)
An invisible creature is impossible to see without the aid of magic or a special sense. For the purpose of hiding, the creature is heavily obscured. The creature’s location can be detected by any noise it makes or any tracks it leaves.
See Invisibility spell (PHB p.274)
For the duration, you see invisible creatures and objects as if they were visible, and you can see into the Ethereal Plane.
Mordenkainen's Faithful Hound spell (PHB p.161)
The hound sees invisible creatures and can see into the Ethereal Plane.
Etherealness spell (PHB p.238)
You can see and hear the plane you originated from, but everything there looks gray, and you can’t see anything more than 60 feet away.
