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The quotation below comes from A Short Story of Arab Peoples by J.B. Glubb, 1969, page 275.
The book say nothing about direct actions against both British or the Turks.
When the Turkish Empire entered the First World War, Ibn Rasheed declared his support for the sultan, while Ibn Saud asked for help from the British government in India. Captain W.H.I Shakespear, then British agent in Kuwait, was sent to Ibn Saud. This gallant officer persuaded Ibn Saud to attack Ibn Rasheed, who threatened to interfere with the British invasion of Iraq. In January 1915, an indecisive battle was fought between the two Arab princes at Jar'ab, in the course of which Shakespear was killed.
Ibn Saud did not move again until 1921, when he finally defeated Ibn Rasheed and became sole ruler of Nejed and Hasa, and the neighbour of King Husain of the Hejaz.
These two paragraphs are the only ones concerning both Hejaz and Nejd of the WW1 times in the book.
There is a Wikipedia article about the mentioned battle of Jarrab, with three references. Maybe you are able to reach them and find more information.