I went off and did some jobs to kill the time. It felt like more than a day had passed but I used the skip time option in the menu to wait 24 hours. I went off and did a couple more side quests and jobs but Takemura still has not rang me. Is this quest glitched?
This quest is glitched, you will more than likely have to restart the game. Depending on the platform, the game might just crash, forcing you to restart. Once you load back into the game from closing it down, he should ring you after a few minutes and you will be able to continue on with the quest.