This is a really interesting horary, mostly because it does set some interpretational challenges.
I firmly agree with Astraea's approach - this is a question that should be settled by the dignity of the neighbour's significator, rather than an aspect. The chart screams change at me - with both your significator, Mercury in the 29th degree and the cusp of the third in the 29th degree You are about to relocate your dwelling to another Landlord shown by Mercury moving from the domicile of Saturn into the domicile of Jupiter and as a consequence the neighbours will change - the third cusp is about to move into Scorpio bringing new neigbours (indeed if you had used any other major house system you would have had a third cusp in Scorpio,
Now if I'd not had the benefit of Astraea's thoughts and got this question 'cold' I'd have used the radical third for the neighbours or possibly thought of using Mars, as the coming neighbours (because of the imminent departure into Scorpio of the third cusp). The question is clearly about the neighbours at the new apartment and the move is already decided, that is the current neighbours are not an issue in this question,,
If you had asked whether the new neighbours would be better than the existing ones then I would totally agree with Astraea in using the third for the existing and the fifth for the new and that's how I would have tackled it. Now she's got me thinking about it LOL
The great thing about horary is that it can be validated - so if the turned version suggests better neighbours than now then experience will show if that's a good choice of the house of the new neighbours.
So, left to myself I would have used Venus for the neighbours in the question and possibly thought about whether I should consider Mars as an alternative. I would not have thought about using the fifth as the house of the new neighbours. However I do see the force of Astraea's argument and I'm having some second thoughts.
Just a couple of questions about the chart's description of the situation:
Is your current Landlord a neighbour or (unlikely) an elder sibling? - Saturn, the current ruler of Mercury sits on the third cusp
If not: In the new apartment will your Landlord be a near neighbour or an elder sibling?
PS: The Moon would not be involved in any translation of light between Mercury and Venus as she will first aspect the Sun before she aspects Mercury thus prohibiting any translation of light.