The club’s former captain has been impressed by the way the South African-based businessman has gone about his business since he and his allies managed to overthrow the old board in March.
King is currently trying to renegotiate the club’s retain contract with Mike Ashley’s Sports Direct firm so that it works better for both parties.
While such things have attracted more attention in the past, fans are devoting more of their attention to how the team itself is performing.
Rangers have started the new season brightly and followed up their 6-2 Petrofac Training Cup win at Hibernian with a one-sided 3-0 League Cup victory over Peterhead on Sunday.
The impact Mark Warburton is having with his new squad is allowing King – who officially took up his position in May – to make progress in the background.
Gough, a friend of his, has been encouraged by the strides being made and said: “I think Dave King has been fantastic. He has been very quiet.
“A lot of people have been asking: ‘Where’s Dave?’ He has been behind the scenes but he is going to put a structure in place that goes a long way to making sure we get back to where we belong.
“What I like about Dave is that the noise level has gone down around Ibrox. The negative press has gone down.
“The last three years you guys have been getting exclusives about what the previous regime have been saying. Now it’s about the football, which is good.
“I know Dave most probably had a meeting with Sports Direct, with Ashley, last week but that doesn’t get publicised. It’s all quiet. We have got to talk about football again.”
Gough was an iconic figure as Rangers won nine league titles in a row in the 1990s and they have fallen a long way since then.
Warburton has recruited sensibly as he has rebuilt a fractured squad, bringing in eight players so far from a variety of clubs in Scotland and England.
As the Ibrox side prepares to start their bid for promotion back to the Scottish Premiership with a home Championship game against St Mirren on Friday, the 53-year-old is optimistic.
Gough added: “There’s a structure behind the football management team which unfortunately wasn’t there in the previous three years.
“It’s going to get put in place slowly, but it has started well. It’s been three years of the club being taken apart. It won’t be a quick fix but the club is going in the right direction.
“I like the way that the management team have gone about it. They haven’t bought anyone for three or four million. It’s like a jigsaw puzzle, putting things together.”