Houses built in 1960 did not require grounds on regular outlets in most of Canada and U.S.A.
Grounds were required on pumps, damp locations, and other special locations. Most of the house was likely wired without pulling ground wires through.
Is this house wired with conduit or non metalic sheathed cable (NMD)?
If it was wired with NMD, it may have the manufactures name, 14/2 or 14/3, 60 oC, NMD3. If it included a ground wire it would include the words with ground. The cable would likely be dirty dark brown, black or green in colour. The main problem is contractors could order NMD cable without writing; this would cost less and many contractor did to reduce costs.
The ground wire if present was to be connected to the box only. Many electricians cut the ground wire so that was just long enough to go under the ground screw. It is very hard to see it unless you remove the device (switch, receptacle, etc) and shine a flashlight into the box. May have to move the wires around. You have to be very careful as the insulation may be getting brittle and break off.
Ungrounded receptacles were banned from sale many years ago in most parts of Canada and U.S.A. As a result, you had to install ground receptacles on ungrounded circuits. I usually fill the ground hole in with epoxy. This identifies the receptacle as ungrounded.
Service entrance grounding was done by 3 main methods:
ground wire was run from the main service entrance disconnect switch's Neutral (Ground wire to be continuous (1 piece - no breaks) from the main service entrance disconnect switch's Neutral)
to:
1/ 2 10 foot galvanized ground rods 10 feet apart outside the house so the top of the rods were 6" below grade. Usually close to the wall, first rod just under the service entrance disconnect switch.
2/ 2 6 foot galvanized ground rods 10 feet apart inside the house in the basement so the top of the rods were 6" below concrete floor. Usually close to the wall, first rod just under the service entrance disconnect switch.
3/ To the supply side of the water supply (before the water meter) if the supply piping was at least 50 feet of 5/8 copper (may vary from area to area)
There are ways to test for substantial grounding. This should be done by a qualified electrician.
Hope this helps
Good Luck