The Constitution did help to "elevate" Gerald Ford. In one case, the elevation was automatic, in the other, it was not.
The 25th Amendment was ratified in 1967. It provided for a new way of selecting a replacement Vice President if such was needed. Instead of simply taking the Speaker of the House, it now allowed the President to select a new Vice President, subject to the approval of both houses of Congress. When Spiro Agnew had to resign as vice president, President Nixon appointed Gerald Ford.
When Nixon himself had to resign, Ford automatically became President. This was because of Article II, Section 1, Clause 6 which provides that the Vice President becomes President if the President is removed, resigns, or dies.