Police communications manager Nic Barclay said the tone of those messages was "goodbye".
"But there's only so much you can take from the tone of a text message."
Based on information from cell towers, the messages were sent from the Catlins area, where the pair had been spotted, Mr Barclay said.
"We had confirmed sightings in the Catlins area and that's where the cell tower was that the text messages pinged off."
During the week before the goodbye text messages were sent, police believed they were staying in rural areas and sleeping in tents and in the car, he said.
Police have said based on track marks at the top of the cliff overlooking Curio Bay, it was believed Mr Beckenridge's car was driven at speed off the top.
Mr Barclay said it would have been "difficult but not impossible" to rig the car to drive itself off the cliff.
"The easiest option...is to tie the [steering] wheel down and shove something on the accelerator.
"These are all possibilities we are looking into, but we can't confirm anything until a) the car's pulled out of the water, or b) we find John and Michael somewhere in the country."
Detective Sergeant Mark McCloy told Radio New Zealand yesterday it would very difficult to rig the car to speed over the cliff by itself.
"It's certainly gone in a particularly straight line, it's left the cliff at a considerable pace, it's been airborne a couple of metres prior to the edge of the cliff.
"The paddock is certainly not smooth - it's rough, hollowed and bumpy."
It would be difficult to drive in a straight line without someone holding onto the wheel, Mr McCloy said.
Mr Barclay said rough weather and tidal conditions had so far made it impossible for the car to be extracted.
Locals had been advising police to stay out of the water at the moment, but they were still assessing the conditions daily.
"We've had moments in the past where we thought we wouldn't have been able to enter the water after a long period of time however the next day the weather had eased up and we were able to enter the water."
Police divers had been able to perform a "partial search" of the station wagon, which showed there was nothing inside.