Hi @Chrisir,
- I made the changes as outlined above regarding the variable color colRect and it now looks as below. And I now understand where I went awry…
Thank you for your guidance with this! 
int gridX = 5;
int gridY = 5;
int many = gridX*gridY; // cells per row and column, # in total
Button [] myButtons = new Button [many]; // declaring Button class array
int r1 = int(random(255));
int g1 = int(random(255));
int b1 = int(random(255));
color background = color ( r1, g1, b1) ; //!!!!!!!!!!!!!!!!!!!!!!!!
void setup() {
size (600, 600);
int x = 40 + 50, y = x, // dist from screen border !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
w = 100, h = w, off = 5; // width and height of one cell, dist btwn cells
int k = 0; // counter for button objects in array
for (int i = 0; i < gridX; i++) { // counter for xpos on grid
for (int i2 = 0; i2 < gridY; i2++) { // counter for ypos on grid
myButtons [k] = new Button ( x + i * (w+off), y + i2 * (h+off),
w, h,
color (random(255), random(255), random(255)), // random colors
color (random(255), random(255), random(255)), // new random colors when on / off toggle
random(50, 125)); // random sizes
k++;
}
}
}
void draw() {
background (background); //!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
for (int i = 0; i < many; i++)
myButtons[i].display();
}
void mouseClicked() {
background = color(random(255), random(255), random(255));
}
void mousePressed() {
for (int i = 0; i < many; i++)
myButtons[i].click ();
}
Button Class ///////////////////
class Button {
float x, y, w, h;
color colRect;
color colRect2;
float sz;
boolean on = false; // button starts in OFF position
Button (float tempX, float tempY,
float tempW, float tempH,
color tempColor, color tempColor2,
float tempSz) {
x = tempX;
y = tempY;
w = tempW;
h = tempH;
colRect = tempColor;
colRect2 = tempColor2;
sz = tempSz;
}
void display() {
if (on) {
fill (colRect2);
noStroke();
} else {
fill (colRect);
noStroke();
}
rectMode(CENTER);
rect(x, y, sz, sz);
}
void click() {
if (mouseX > x - sz/2 && // !!!!!!!!!!!!!!!!
mouseX < x + sz/2 &&
mouseY > y - sz/2 &&
mouseY < y + sz/2 )
on = !on; // toggle on / off
}
}