Gilzean, who was recently diagnosed with a brain tumour, became known as "The King of White Hart Lane" after joining Spurs in 1964.
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Kenny Miller grabbed his first goal in five months as Rangers fired themselves back up to second spot with a 4-0 victory over Dundee at Ibrox.
Celtic's drive to the Ladbrokes Premiership title hit an unexpected speed bump with a goalless draw against relegation battlers Dundee at Parkhead.
Celtic moved 11 points clear of Aberdeen at the top of the Scottish Premiership with a businesslike 2-0 Boxing Day win over Dundee at Dens Park.