Murdoch is one of four men - alongside Paul Murray, Malcolm Murray and Alex Wilson - that hope to win seats at the Light Blues top table at the AGM on December 19.
New CEO Wallace, chairman David Somers and non-executive director Norman Crighton are all up for re-election alongside Sandy Easdale and Stockbridge.
"There are two things they can do [to prove their independence]," Murdoch told TheCoplandRoad.org
"They can tell us how they got appointed. Were they appointed by Brian Stockbridge? Who brought them on board? How did David Somers get selected?
"Secondly, if they are independent then they will presumably realise that under the financial control of Brian Stockbridge, and aside from his personal conduct, the company performance has been appalling.
"Stockbridge predicted a £7million loss which in fact became a £14m loss only three months after he made the prediction.
"He is clearly incapable. If you were independent then surely you would ask him to leave?
"I don't think Wallace will do himself any favours if he nails his colours to the Stockbridge mast.
"If he takes him to the AGM with him then he's effectively doing that.
"If you ask me what I'd do if I was Graham Wallace then I'd suggest to Stockbridge that he falls on his sword.
"He is without question directly linked with Imran Ahmad and Charles Green and he's got to go."
The four Requisitioners will have the backing of the majority of Gers fans at the make-or-break shareholder summit but must convince the institutional investors in Rangers International Football Club plc that they are the right men to lead the Glasgow giants.
Wilson has dismissed claims the current board could command around 70% of the vote at the AGM and insists the Murray-led alliance has fresh investment lined up should they win power.
"We know how we want to operate but what we find when we get in there is impossible to say," Wilson told The Rangers Standard.
"When we lift the lid on it we have no idea what is going to come out.
"What worries us is that there is a cash outflow which has not been explained, so we need to look at what we have and then start to address it urgently.
"We can't say specifically who will invest. We have 3-4 people who are wealthy individuals who have approached us and said they will put money into the club if the board is trustworthy and clean.
"We've also had some of the institutions, who we can't name for reasons of confidentiality; tell us they will put more money in. We just can't put names into the public domain at this time as frustrating as that might be for people."