SVG animation delay on each repetition

Define dummy loop and set relative start time. See How to make SVG Loop Animation?

<svg xmlns="http://www.w3.org/2000/svg" width="300px" height="200px">
  <rect>
    <animate id="o1" begin="0;o1.end" dur="10s"
    attributeName="visibility" from="hide" to="hide"/>
  </rect>
  <circle fill="orange" cx="-50" cy="100" r="20">
    <animate begin="o1.begin" 
    attributeName="cx" from="250" to="50" dur="5.05s"/>
  </circle>
  <circle fill="blue" cx="150" cy="100" r="50" />
  <circle fill="orange" cx="-50" cy="100" r="20">
    <animate begin="o1.begin+5s" 
    attributeName="cx" from="50" to="250" dur="5.05s"/>
  </circle>
</svg>

Below an example of "closing eyes"... thanks to the suggestions in this thread.

<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 80 16"><g>
  <g >
  <ellipse cx="9.45" cy="7.7" rx="0.96" ry="0.96" style="stroke: none; fill: black;">
   <animate id="op" attributeName="ry" attributeType="XML"
             to="0.1"
             begin="3s;op.end+3s" dur="0.15s"
             fill="remove" repeatCount="2"
            />
  </ellipse>
  <ellipse cx="14.6" cy="7.8" rx="0.8" ry="0.8" style="stroke: none; fill: black;">
   <animate id="op" attributeName="ry" attributeType="XML"
             to="0.1"
             begin="3s;op.end+3s" dur="0.15s"
             fill="remove" repeatCount="2"
            />
  </ellipse>
 </g>
</svg>

You can add the end event of a SMIL animated element to the begin attribute.
Also, you can add multiple values, separated by ; to this begin attribute :

<svg xmlns="http://www.w3.org/2000/svg" width="300px" height="100px">
  <circle cx="50" cy="50" r="15" fill="blue">
    <animate id="op" attributeType="CSS" attributeName="opacity"
             from="1" to="0" dur="3s" begin="3s;op.end+3s" />
  </circle>
</svg>