For much of the day, Arjay can be seen going about the city, purchasing the items that he would need. The spell wasn't particularly hard to come by, he'd had a few copies of it left among his personal effects, thankfully. He'd had to go buy the incense, though, and it had taken a fair amount of scrounging to come across the strips of ivory. But at the end of the day, he had everything, and after getting the information he needed from Cadence, he prepared himself and shut himself away in his room, lighting the incense and arranging the slips of ivory as he began a very long spellcasting.
The innkeeper would turn away any visitors asking for him, save for a select few who were allowed to check on him once a day. Any who made it in would find him focused on the spell, completely ignoring anyone who came in. He would not reply to any urgings to eat or rest, nor would he respond to any questions. Anyone who forced him to break his concentration... well, would probably be met with a rather angry reply (and possibly a black eye) for forcing him to have to start all over again.
((roll of 1d10 days resulted in: 2 days. Arjay won't be seen in-game for the duration))