Instructions
Go to the Government Laboratory between 8:00 AM and 4:00 PM on Monday or 4:00 PM and midnight on Saturday. It's located in the basement. Walk to the northwest corner and interact with the floating blue icon to get your first Mechanical skill point.
Enter Mamma Hogg's bedroom between 4:00 PM and midnight on Monday. The Mechanical icon is floating over the shrine to Auda Sherif. The exact location of Mamma Hogg's bedroom varies, depending on which guest room you assigned her to.
Walk to the Furnace Room between 4:00 PM and midnight on Tuesday or 8:00 AM and 4:00 PM on Thursday. It's in the basement, to the left of the staircase. The skill point is floating above the pallet.
Climb down the stairs to the basement between 4:00 PM and midnight on Thursday. You'll find the Mechanical point floating by the staircase.
Take the elevator to the Atrium Center between midnight and 8:00 AM on Saturday. You'll find the Mechanical point in the alcove.