To find the value of $a$ for which the line has equal intercepts on both axes, we will find the $x$-intercept and the $y$-intercept of the line.

**For the $x$-intercept:**
We set $y = 0$ to find where the line intersects the $x$-axis:
$$ax + (0) - 2 - a = 0$$
$$ax - a - 2 = 0$$
$$ax = a + 2$$
If $a \neq 0$, the $x$-intercept is:
$$x = \frac{a + 2}{a}$$

**For the $y$-intercept:**
We set $x = 0$ to find where the line intersects the $y$-axis:
$$(0) \cdot a + y - 2 - a = 0$$
$$y = 2 + a$$

For the intercepts to be equal:
$$\frac{a + 2}{a} = 2 + a$$

Now we solve for $a$:
$$a^2 + 2 = 2a + a^2$$
$$a = -2 \text{ or } a = 1$$

So the values of $a$ for which the line $l$ has equal intercepts on both the $x$-axis and the $y$-axis are $\boxed{-2 \text{ or } 1}$.