Seemingly born in the Newington area of Edinburgh, as far as I can find out the earliest football played by Bob was with Edinburgh Myrtle in East of Scotland Junior football, where he had impressed enough for Queen's Park to pick him up in 1903/04. From the middle of December he played regularly with the Spiders in Inside-Forward and Center-Forward positions for the next month, playing 6 and scoring twice while at Mount Florida.
Whether or not Hibs actually signed him next or simply played him is unknown. I have no way of knowing whether he was a fixture in the reserves in between his 2 appearances for the club, or whether he was a "free man". The latter is possible, especially in the light that his matches were in two different seasons. Robert had scored on his debut, but neither this nor his second game [both, incidentally against Kilmarnock] were enough to convince those in charge that he was worth continuing with [it must be said that he was about 25 by this time].
Curiously enough, four weeks after his last appearance for Hibs, Robert was in the Hearts line-up against Hibs on the 29th Oct 1904 for what seems to be his only appearance for the Jambos.
His situation at Hearts was clearly only temporary [perhaps a loan?] because on Christmas Eve 1904 Robert Stalker was now playing Centre-Forward for Falkirk at Abercorn [scoring twice], and there he stayed for the next three matches until Jan 14th 1905 [scoring another brace v Albion Rovers the previous week].
Yet, within the week the SFA has Bob listed as signing for his fourth team of the season [it is now impossible to play for more than two without UEFA's special permission], when he turned out for Motherwell in two league matches.
Toward the end of the season an R.Stalker again played for Falkirk v St Bernards in an East of Scotland League match, this was probably the same player but I am not 100% sure.
From this point on it seems that he disappeared from senior football in Scotland, and apart from a single game for St Bernards in the 1907 Roseberry Charity Cup possibly from all football [though I suspect he may have returned to the junior folds], suggesting that football was not his first priority.
So, what to make of such a short and transient career? There are two possibilities. 1) going on from his time that he was with Queen's Park, Robert was an amateur with employment elsewhere which did not allow him to devote the time to full-time football, but was good enough for several clubs to desire his services where and when or 2) after his time at QP he signed for Hibernian who after failing to find a place for him subsequently loaned him out to whoever needed him for the rest of the season.
While the former sounds nice and romantic, the fact that he effectively dissappeared from football after 1904/05 seems that he either was too busy in his 'other' employment or that he never found a place in football [whether through injury or lack of ability I cannot tell], but it points toward the latter.
Nearly two decades after his time in football  I found Robert on a ship's manifest from Scotland to Boston, he described himself as a 46 year old 'house-painter' and gave his previous address as '2 Merchiston Place, Edinburgh", within 4 years he is found in the Philadelphia Census, and was then a 51 year old 'golf professional'.
This raises the possibility that he was mainly a golfer [and not a footballer] in his youth, possibly explaining his sporadic appearances, and it is to an extent borne out by his obituary in the Philadelphia Inquirer [December 13th 1930] which stated that he was "the coach for Andrew Jamieson who defeated Bobby Jones in 1926."
But the simple fact is that his passing went, as far as I can tell, largely unnoticed by the majority of Scottish Football, however, he hardly set Scottish Football on fire.
b 1879-1880, Edinburgh
d 11th December 1930, Abington, Pennsylvania, USA
Positions – Centre-Forward, Inside-Left, Inside-Right
Queen's Park [1903/04]
Scottish League Matches/Goals [6/2]
Scottish League Matches/Goals [2/1]
Heart of Midlothian [1904/05]
Scottish League Matches/Goals [1/-]
Scottish League Matches/Goals [4/4]
EoS League Matches/Goals [1/-]
Scottish League Matches/Goals [2/-]
St Bernards [1906/07]
Roseberry Charity Cup Matches/Goals [1/-]
Height – 5” 7½'