The cleanout would typically be at the base of the main plumbing stack and/or just inside or outside the home. When located outside, it's common for them to get buried over with landscaping. You should also have one every 100' to the connection with the municipal sewer. When located inside, they may be in the wall with a removable cover on the drywall instead of a large plug in the floor.
That said, I believe most plumbers would just pull the toilet and snake it from there. You know the clog is downstream of that toilet, and you know that all drain connections from the toilet down should be at least 3" to run a large snake down the line.
Here a bit more of the requirements for a cleanout from the 2012 plumbing code which I doubt have changed much since your home was built (mine in the early 1980s has the cleanout at the base of the stack and another in the front yard). Note there are lots of exceptions, like not requiring cleanouts for anything above the bottom floor of the residence that can be found in the source link:
2012 International Plumbing Code - Cleanout requirements:
IPC - Section 708 Cleanouts
IPC - 708.1 Scope. This section shall govern the size, location,
installation and maintenance of drainage pipe cleanouts.
IPC - 708.2 Cleanout plugs. Cleanout plugs shall be brass or plastic,
or other approved materials. Brass cleanout plugs shall be utilized
with metallic drain, waste and vent piping only and shall conform to
ASTM A 74, ASME A112.3.1 or ASME A112.36.2M. Cleanouts with
plate-style access covers shall be fitted with corrosion-resisting
fasteners. Plastic cleanout plugs shall conform to the requirements of
Section 702.4. Plugs shall have raised square or countersunk square
heads. Countersunk heads shall be installed where raised heads are a
trip hazard. Cleanout plugs with borosilicate glass systems shall be
of borosilicate glass.
IPC - 708.3 Where required. Cleanouts shall be located in accordance
with Sections 708.3.1 through 708.3.6.
IPC - 708.3.1 Horizontal drains within buildings. All horizontal
drains shall be provided with cleanouts located not more than 100 feet
(30 480 mm) apart.
IPC - 708.3.2 Building sewers. Building sewers shall be provided with
cleanouts located not more than 100 feet (30 480 mm) apart, measured
from the upstream entrance of the cleanout. For building sewers 8
inches (203 mm) and larger, manholes shall be provided and located not
more than 200 feet (60 960 mm) from the junction of the building drain
and building sewer, at each change in direction and at intervals of
not more than 400 feet (122 m) apart. Manholes and manhole covers
shall be of an approved type.
IPC - 708.3.3 Changes of direction. Cleanouts shall be installed at
each change of direction greater than 45 degrees (0.79 rad) in the
building sewer, building drain and horizontal waste or soil lines.
Where more than one change of direction occurs in a run of piping,
only one cleanout shall be required for each 40 feet (12 192 mm) of
developed length of the drainage piping.
IPC - 708.3.4 Base of stack. A cleanout shall be provided at the base
of each waste or soil stack.
IPC - 708.3.5 Building drain and building sewer junction. There shall
be a cleanout near the junction of the building drain and the building
sewer. The cleanout shall be either inside or outside the building
wall and shall be brought up to the finished ground level or to the
basement floor level. An approved two-way cleanout is allowed to be
used at this location to serve as a required cleanout for both the
building drain and building sewer. The cleanout at the junction of the
building drain and building sewer shall not be required if the
cleanout on a 3-inch (76 mm) or larger diameter soil stack is located
within a developed length of 10 feet (3048 mm) of the building drain
and building sewer connection. The minimum size of the cleanout at the
junction of the building drain and building sewer shall comply with
IPC - 708.3.6 Manholes. Manholes serving a building drain shall have
secured gas-tight covers and shall be located in accordance with
IPC - 708.4 Concealed piping. Cleanouts on concealed piping or piping
under a floor slab or in a crawl space of less than 24 inches (610 mm)
in height or a plenum shall be extended through and terminate flush
with the finished wall, floor or ground surface or shall be extended
to the outside of the building. Cleanout plugs shall not be covered
with cement, plaster or any other permanent finish material. Where it
is necessary to conceal a cleanout or to terminate a cleanout in an
area subject to vehicular traffic, the covering plate, access door or
cleanout shall be of an approved type designed and installed for this
IPC - 708.5 Opening direction. Every cleanout shall be installed to
open to allow cleaning in the direction of the flow of the drainage
pipe or at right angles thereto.
IPC - 708.6 Prohibited installation. Cleanout openings shall not be
utilized for the installation of new fixtures, except where approved
and where another cleanout of equal access and capacity is provided.
IPC - 708.7 Minimum size. Cleanouts shall be the same nominal size as
the pipe they serve up to 4 inches (102 mm). For pipes larger than 4
inches (102 mm) nominal size, the size of the cleanout shall be not
less than 4 inches (102 mm).