what is the historical origin of the installation ritual for a worshipful master and how did the esoteric or 'inner' part develop

The formal order for installing a Worshipful Master was documented in the early eighteenth century, with James Anderson recording the procession used at installations from 1724 2. By the late eighteenth century, William Preston outlined the standard procedure for installing a Master, which included presenting the Master-elect at the pedestal, reading the fifteen ancient charges and six regulations for his assent, and delivering a formal address upon his invested authority 1.

The esoteric or inner portion of the ceremony—conducted when the lodge is opened in a Board of Installed Masters or Past Master Lodge—belongs to the private workings of the lodge. These inner modes and communications are received in the lodge from one brother to another and are not set down in published texts.

Historical lodge records illustrate how the separate inner working functioned in practice during the nineteenth century. In 1852, lodge minutes record a Worshipful Master requesting all Master Masons to retire so the Master-elect could be installed in a Past Master Lodge 3. The status of this inner ceremony was subject to debate in some jurisdictions, as contemporary objections noted that late Masonic records had questioned or declared a distinct "Past Master degree" illegal, even while recognizing that an installed Master held the essential qualification to preside and confer degrees 3.

The formal organization of a Board of Installed Masters began in the early nineteenth century during efforts to regularize ritual prior to and following the 1813 Union in England. Brethren formed a Board of Installed Masters on 16 November 1810 to conduct the ceremony of installation during the proceedings of the Lodge of Promulgation, as a paper read before Quatuor Coronati Lodge records.

Following the Union of the Moderns and Antients Grand Lodges, a Lodge or Board of Installed Masters was formally established in 1827 to standardize the installation ceremony and oversee its delivery, from which the modern widely followed procedure derives, according to a paper read before Quatuor Coronati Lodge.

The installation procedure set out in William Preston's account from 1796 does not describe a Board of Installed Masters. Preston's published sequence for installing a Worshipful Master focuses on the constitutional and ceremonial framework: the Deputy presents the Master-elect at the pedestal, the Secretary reads the fifteen ancient charges and six regulations, the candidate signifies his assent, and the presiding officer delivers the formal investiture and address 1.

While Preston outlines the consecration of the lodge, the presentation of the candidate, and the assent to the charges 1, his text makes no mention of opening a separate Board or Lodge of Installed Masters for an inner ceremony 1. That formal structure developed later, in the early nineteenth century, as part of the ritual standardization undertaken around the 1813 Union.

The websites I drew on here are not among those a Masonic researcher would ordinarily rely upon. Please weigh what they say accordingly.