I know the temptation is to get into the dialogue and start to build the interaction quickly - I write a bit myself, but I would sugest a few more seconds of scene building, something like -

He made no sound moving over the ornately patterned carpet as he strode into the sitting room, and was halted by the glassy stare of a multitude of porcelain dolls, which stood, sat or reclined on ... give impression of the decoration/furniture.

Reflecting the (describe window to infer architecture of house and weather outside) was a confection of a clock. He moved closer so as to see past the reflection and make out the face and hands, then glanced at his watch. (the clock either surprises him by being correct, or is showing the wrong time)

As he surveyed the complex interior of the case, the looped chains and suspended weights, the pendulum weight cast in the shape of a horse and rider, the sound of the tick began to grate on his nerves.

He moved away a step, and the glass of the clock case now reflected his own image - describe. He straightened his tie before he turned away, and was startled again to find that he was facing a pair of very living eyes, those of a (short first impression of the woman) who held part of what might be a sock, impaled by several long slender needles. She almost smiled.

You see that you can put in a lot about the situation, rather than having the two people meet in an undefined space and time by working the light within a room, and also create a frisson between them using the little gesture of him straightening his tie and turning to find he is observed.

I am a little doubtful about introducing the unusual names so early - would a woman ask a man she just met in a professional capacity what his given names were - particularly if she knew they were unusual and would almost certainly embarass him?

Also being slightly more veiled about why Josh would not come to the house, maybe introduce the haunted information only as they go upstairs, so she can turn around and they be eye to eye as she accuses him of being 'one of those' due to her being two steps ahead of him.

I would have thought that she should give him and the reader, some information about who was dead upstairs and who was living, and banging on the ceiling whilst still in the downstairs room.

These are pretty standard plot development ploys - there is quite a lot of information available on 'plotting' and 'characterisation' - people do write books about writing books - you might be able to get some through your local library.